Polygons Test - 1

It is given that the measure of each interior angle of the polygon is 108°.

∴Measure of each exterior angle of the polygon = 180° − 108° = 72°

The sum of the measures of all exterior angles of any convex polygon is 360°.

Thus, number of exterior angles of the polygon = 360⁰/72⁰ = 5

Since the polygon has five exterior angles, it also has five sides.

Hence, the polygon is a pentagon.

Sum of interior angles of polygon = 180 (n − 2) where n = number of sides

In a regular hexagon, there are 6 sides and all angles are equal.

Therefore, sum of interior angles of a regular hexagon = 180 × (6 − 2)

= 180 × 4

= 720°

Therefore, measure of each angle of a regular hexagon = 720⁰/6 = 120⁰

An angle measuring 120⁰ is an obtuse angle.

A square is a rhombus because its opposite sides are parallel and all sides are equal

A square is a rectangle because it has four sides and four right angles

A square is a parallelogram because its opposite sides are parallel

A hexagon is a closed figure with six sides but a square has four sides. Therefore, a square is not a hexagon

The sum of the angles of a quadrilateral is 360°

∴ xº + (3x − 40)º + (2x)º + (4x + 20)º = 360º

(10x − 20)º = 360°

(10x)º = 360° + 20º

(10x)º = 380°

x = 38°

Thus, the measures of the angles of the quadrilateral are:

x = 38°

(3x − 40)º = (3 × 38 − 40)° = 74°

(2x)º = (2 × 38)° = 76°

(4x + 20)º = (4 × 38 + 20)° = 172°

Thus, the measure of the largest angle is 172°.

An equiangular polygon is one in which each internal angle is of the same measure. An equilateral polygon is one in which each side is of the same length. Thus, a regular polygon is both equiangular and equilateral.

Therefore, only statement 3 is correct.

Since the given polygon has 12 sides, it also has 12 exterior angles.

In a regular polygon, all interior angles are of equal measure. Thus, all exterior angles of the polygon are also of equal measure.

The sum of the measures of all exterior angles of any convex polygon is 360°.

Thus, measure of each exterior angle of the given polygon = 360⁰/12 = 30⁰.