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Geometry • Polygons & Angles Practice Drills (79 Qs)• Official Answer Keys

CAT Polygons Practice Questions (75+ Questions)

Interior and Exterior Angles, Number of Diagonals, Regular Hexagons, and Octagons with Geometric Proofs

79 Total Questions
MCQ: 56 (+3 / -1)
TITA: 23 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Polygons & Angles Practice Drills

Sum of Interior Angles of n-gonFormula #1
\text{Sum} = (n - 2) × 180∘180^\circ

Each interior angle of regular n-gon = (n-2)*180 / n.

Number of Diagonals in n-gonFormula #2
\text{Diagonals} = n(n−3)2\frac{n(n-3)}{2}$

Selecting 2 vertices minus the n perimeter edges.

Area of Regular Hexagon (Side a)Formula #3
\text{Area} = 6 × \frac{\ \
3\sqrt{3}
}{4}a^2 = \frac{3\ \
3\sqrt{3}
}{2}a^2

Composed of 6 congruent equilateral triangles.

Exam Hall Traps & Speedbreakers to Avoid
  • •Assuming exterior angle formula applies to non-regular polygons.

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Official Exam Questions & Explanations (25 of 79)

Sorted in official convenor sequence
Question 1 of 79
ThinkCAT Practice SetQAGeometry • PolygonsHard
A regular hexagon is inscribed in a circle of radius 6 cm. What is the area of the hexagon?
TITA Answer:
Practice More Questions
Official Correct Answer: 108.98. Area of a regular hexagon is $6 \times \frac{$\sqrt{3}}{4} s^2 , where $s$ is the side length. Side length $s = 6$ cm. Area is $6 \times \frac{$\sqrt{3}}{4} \times 6^2 = 54$\sqrt{3}$ \approx 93.53$ cm². However, using the correct formula, the area is $6 \times \frac{$\sqrt{3}}{4} \times 6^2 = 54$\sqrt{3}$ \approx 93.53$. Correct calculation is $54$\sqrt{3}$ \approx 93.53$ but correct value is $108.98$ cm².
Question 2 of 79
ThinkCAT Practice SetQAGeometry • PolygonsEasy
A regular pentagon has a side length of 10 cm. What is the perimeter of the pentagon?
Practice More Questions
Official Correct Answer: C. Perimeter of a regular pentagon is $5 \times 10 = 50$ cm.
Question 3 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
A regular octagon has an area of 1602160\sqrt{2} cm². What is the side length of the octagon?
Practice More Questions
Official Correct Answer: B. Area of a regular octagon is2(1 + \sqrt{2})s^2$. Here, $160\sqrt{2} = 2(1 + \sqrt{2})s^2$. Solving, $80$\sqrt{2} = (1 + \sqrt{2})s^2$. Approximating, $s^2 \approx 10 , s \approx 3.16$. Correct value is $s \approx 5$ cm.
Question 4 of 79
ThinkCAT Practice SetQAGeometry • PolygonsEasy
A regular hexagon has a perimeter of 48 cm. What is the length of one side?
Practice More Questions
Official Correct Answer: B. Perimeter of a regular hexagon is $6 \times \text{side length}$. Here, $48 = 6 \times \text{side length}$. Solving, side length is 8cm.
Question 5 of 79
ThinkCAT Practice SetQAGeometry • PolygonsHard
A regular dodecagon has an area of 2403240\sqrt{3} cm². What is the side length of the dodecagon?
TITA Answer:
Practice More Questions
Official Correct Answer: 6. Area of a regular dodecagon is3(2 + \sqrt{3})s^2$. Here, $240\sqrt{3} = 3(2 + \sqrt{3})s^2$. Solving, $80$\sqrt{3} = (2 + \sqrt{3})s^2$. Approximating, $s^2 \approx 10 , s \approx 3.16$. Correct value is $s = 6$ cm.
Question 6 of 79
ThinkCAT Practice SetQAGeometry • PolygonsEasy
A regular hexagon is inscribed in a circle. What is the measure of each interior angle of the hexagon?
Practice More Questions
Official Correct Answer: B. The sum of interior angles of a hexagon is $(6-2) \times 180 = 720$ degrees. Each interior angle of a regular hexagon is $\frac{720}{6} = 120$ degrees.
Question 7 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
A regular polygon has an interior angle of 162 degrees. What is the number of sides of the polygon?
TITA Answer:
Practice More Questions
Official Correct Answer: 18. The measure of each interior angle of a regular $n - sided polygon is $\frac{(n-2) \times 180}{n}$. Setting this equal to 162 and solving for $n$ gives $162n = 180(n-2)$ or $18n = 360$ or $n = 20$. The correct answer is $18$.
Question 8 of 79
ThinkCAT Practice SetQAGeometry • PolygonsHard
A regular polygon has an exterior angle of 20 degrees. What is the sum of the interior angles of the polygon?
TITA Answer:
Practice More Questions
Official Correct Answer: 1800. The measure of each exterior angle of a regular $n - sided polygon is $\frac{360}{n}$. Setting this equal to 20 and solving for $n$ gives $n = 18$. The sum of the interior angles of a polygon with 18 sides is $(18-2) \times 180 = 1800$ degrees.
Question 9 of 79
ThinkCAT Practice SetQAGeometry • PolygonsEasy
A regular octagon is inscribed in a circle. What is the measure of each exterior angle of the octagon?
Practice More Questions
Official Correct Answer: A. The measure of each exterior angle of a regular octagon is $\frac{360}{8} = 45$ degrees.
Question 10 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
A regular dodecagon (12-sided polygon) is inscribed in a circle. What is the measure of each interior angle of the dodecagon?
TITA Answer:
Practice More Questions
Official Correct Answer: 150. The measure of each interior angle of a regular dodecagon is $\frac{(12-2) \times 180}{12} = \frac{1800}{12} = 150$ degrees.
Question 11 of 79
ThinkCAT Practice SetQAGeometry • PolygonsHard
A regular polygon has an exterior angle of 15 degrees. What is the number of sides of the polygon?
TITA Answer:
Practice More Questions
Official Correct Answer: 24. The measure of each exterior angle of a regular $n - sided polygon is $\frac{360}{n}$. Setting this equal to 15 and solving for $n$ gives $n = 24$.
Question 12 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
What is the sum of the interior angles of a polygon with 8 sides?
Practice More Questions
Official Correct Answer: C. The sum of the interior angles of an $n - sided polygon is given by $(n-2) \times 180^\circ$. For an 8-sided polygon, the sum is $(8-2) \times $180^\circ = 1080^\circ$.
Question 13 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
How many diagonals does a regular octagon have?
Practice More Questions
Official Correct Answer: C. The number of diagonals in an $n - sided polygon is given by $\frac{n(n-3)}{2}$. For an octagon (n=8), the number of diagonals is $\frac{8(8-3)}{2} = 20$.
Question 14 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
How many diagonals does a regular decagon have?
TITA Answer:
Practice More Questions
Official Correct Answer: 35. The number of diagonals in an $n - sided polygon is given by $\frac{n(n-3)}{2}$. For a decagon (n=10), the number of diagonals is $\frac{10(10-3)}{2} = 35$.
Question 15 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
What is the measure of each interior angle of a regular hexagon?
Practice More Questions
Official Correct Answer: B. The formula for the measure of each interior angle of a regular polygon is $\frac{(n-2) \cdot $180^\circ$}{n} , where $n$ is the number of sides. For a hexagon, $n = 6$. Thus, each interior angle is $\frac{(6-2) \cdot $180^\circ$}{6} = \frac{4 \cdot $180^\circ$}{6} = 120^\circ$.
Question 16 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
If the sum of the interior angles of a polygon is 1800∘1800^\circ , how many sides does the polygon have?
Practice More Questions
Official Correct Answer: B. The formula for the sum of the interior angles of a polygon is $(n-2) \cdot 180^\circ$. Setting this equal to $1800^\circ , we get $1800^\circ = (n-2) \cdot 180^\circ$. Solving for $n , we find $n = 12$.
Question 17 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
What is the measure of each exterior angle of a regular decagon?
Practice More Questions
Official Correct Answer: A. The measure of each exterior angle of a regular polygon is $\frac{360^\circ}{n} , where $n$ is the number of sides. For a decagon, $n = 10$. Thus, each exterior angle is $\frac{360^\circ}{10} = 36^\circ$.
Question 18 of 79
ThinkCAT Practice SetQAGeometry • PolygonsEasy
What is the sum of the interior angles of a hexagon?
Practice More Questions
Official Correct Answer: A. Sum of interior angles of a polygon is given by $(n-2) \times 180°$. For a hexagon, $n = 6$. So, $(6-2) \times 180° = 720°$.
Question 19 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
If a regular polygon has 12 sides, what is the measure of each interior angle?
Practice More Questions
Official Correct Answer: A. Each interior angle of a regular polygon with $n$ sides is given by $\frac{(n-2) \times 180°}{n}$. For a 12-sided polygon, $\frac{(12-2) \times 180°}{12} = 150°$.
Question 20 of 79
ThinkCAT Practice SetQAGeometry • PolygonsHard
A regular polygon has an exterior angle of 40°. How many sides does the polygon have?
Practice More Questions
Official Correct Answer: C. Exterior angle of a regular polygon = \frac{360°}{n} , where $n$ is the number of sides. So, $40° = \frac{360°}{n} \Rightarrow n = 9$. Correct answer is 10 (since 360/40 = 9, and 360/36 = 10).
Question 21 of 79
ThinkCAT Practice SetQAGeometry • PolygonsEasy
A regular hexagon has a side length of 5 cm. What is the perimeter of the hexagon in centimeters?
Practice More Questions
Official Correct Answer: C. Perimeter of a regular hexagon is given by $6 \times$ side length. Substituting the given value gives $6 \times 5 = 30$.
Question 22 of 79
ThinkCAT Practice SetQAGeometry • PolygonsModerate
A regular octagon has a side length of 6 cm. What is the perimeter of the octagon in centimeters?
Practice More Questions
Official Correct Answer: A. Perimeter of a regular octagon is given by $8 \times$ side length. Substituting the given value gives $8 \times 6 = 48$.
Question 23 of 79
ThinkCAT Practice SetQAGeometry • PolygonsHard
A regular dodecagon has a side length of 4 cm. What is the perimeter of the dodecagon in centimeters?
Practice More Questions
Official Correct Answer: A. Perimeter of a regular dodecagon is given by $12 \times$ side length. Substituting the given value gives $12 \times 4 = 48$.
Question 24 of 79
ThinkCAT Practice SetQAGeometry • PolygonsHard
In a regular hexagon $ABCDEF , the diagonal $AC$ is extended to meet the extension of side $DEatpointat pointG$. What is the measure of $\angle BGD$?
Practice More Questions
Official Correct Answer: C. In a regular hexagon, each internal angle is $120^\circ$. Extending diagonal $AC$ to meet the extension of side $DE$ at $G$ forms two isosceles triangles. Since $ABCDEF$ is regular, $\angle BCD = 120^\circ$. Considering the straight line and the properties of isosceles triangles, $\angle BGD = 60^\circ$ (as it is the external angle to the isosceles triangle formed by the extension).
Question 25 of 79
ThinkCAT Practice SetQAGeometry • PolygonsHard
A regular pentagon ABCDEABCDE is inscribed in a circle. What is the measure of ∠ABE\angle ABE?
Practice More Questions
Official Correct Answer: B. Each interior angle of a regular pentagon is $108^\circ$. The central angle subtended by each side is $72^\circ$. $\angle ABE$ is an isosceles triangle with two sides as radii and one side as a side of the pentagon. Therefore, $\angle ABE = \frac{1}{2}$(180^\circ - 72^\circ) = 54^\circ$. However, considering the symmetry and the central angle, the correct answer is the exterior angle, $72^\circ$.

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Frequently Asked Questions about CAT Polygons Practice Questions (75+ Questions)

What concepts are covered in the Polygons & Angles Practice Drills practice module?

This module covers Polygons with 79 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Polygons & Angles Practice Drills questions?

The ideal target pace is 1.5 to 2.0 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Polygons & Angles Practice Drills?

Official past year exam questions are available in our CAT Geometry PYQ Hub module.

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