Practice the questions given in the worksheet on interior angles of a polygon.

We know, the sum of all the interior angles of a polygon is (n – 2) × 180°. The questions are based on finding the sum of the interior angles of a polygon using the formula.

**1.** Is it possible to have a polygon whose sum of the interior angles is:

(a) 720°

(b) 840°

(c) 1080°

(d) 620°

(e) 22°

**2.** Is it possible
to construct a polygon, the sum of whose interior angles is 20 right angles? If
yes, find the number of sides of the polygon.

**3.** The angle of a
hexagon are in the ratio 1 : 2 : 3 : 4 : 6 : 8. Find the measure of the
smallest and the biggest angles.

**4.** One of the
angle of a polygon is 100° and each of the other angles is 110°. Find the
number of sides in the polygon.

**5.** The ratio of
number two sides of two regular polygons is 3 : 4 and the ratio of the sum of
their interior angles is 1 : 2. Find the number of sides of each polygon.

**6.** The four angle
of a hexagon are 60°, 90°, 150° and 180° and the other two angles are equal.
Find the measure of these equal angles.

**7.** The measure of
four angles of a heptagon is equal and the measure of the other three angles is
120° each. Find the measure of unknown angles.

**8.** The four angle
of a pentagon are equal and the fifth angle measure 140°. Find the measure of
four equal angles.

**9.** The seven
angle of an octagon are 132° each. Find the measure of the eighth angle.

**10.** The angles of
a pentagon are x°, (x – 5)°, (x + 15)°, (3x – 44)° and (x – 70)°. Find x.

**11.** The angle of
a pentagon are (x – 1)°, (x – 2)°, (x – 3)°, (x – 4)° and (x – 5)° . Find the
value of x and the measure of all angles.

**12.** Four of the
angles of a pentagon are equal. The fifth angle is 40°. Find the angles.

**13.** Each interior
angle of a polygon is 150°. Find the sum of interior angles of a polygon which
has half the number of sides of the given polygon.

Answers for the worksheet on interior angles of a polygon are given below to check the exact answers of the above questions.

**Answers:**

**1.** (a) Yes

(b) No

(c) Yes

(d) No

(e) No

**2.** Yes, 12

**3.** Smallest angle
= 30° and biggest angle = 240°

**4.** 5

**5.** 3, 4

**6.** 120°

**7.** 135°

**8.** 100°

**9.** 156°

**10.** 92

**11.** 111°, 110°,
109°, 108°, 107° and 106°

**12.** 125°, 125°,
125°, 125° and 40°

**13.** 720°

**● **Polygons - Worksheets

**Worksheet on Polygon and its Classification**

**Worksheet on Interior Angles of a Polygon**

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