Question

In the figure below, a shaded polygon, which has equal sides and equal angles, is partially covered with a sheet of blank paper. If x + y = 80, how many sides
does the polygon have?

Answer 1

Answer:

The polygon has 9 sides ⇒ D

Step-by-step explanation:

This is a tricky question

∵ The shaded figure is a quadrilateral

∴ The sum of the measures of its angles is 360

∵ Its angles are x, y, and two vertices of the polygon

∵ All angles of the polygon are equal in mesures

∴ x + y + m of 2 vertices = 360°

∵ x + y = 80

→ Substitute the value of x + y above by 80

∴ 80 + m of 2 vertices = 360

→ Subtract 80 from both sides

∴ m of 2 vertices = 280

→ Divide the two sides by 2

∴ m of 1 vertex = 140°

∴ The measure of each angle of the polygon is 140°

The sum of the measures of the interior angle and the exterior angle at any vertex of the polygon is 180°

∵ m of interior ∠ + m of exterior ∠ = 180° ⇒ at any vertex

∴ 140 + m of exterior ∠ = 180°

→ Subtract 140 from both sides

∴ m of exterior ∠ = 40°

∴ The measure of each exterior angle is 40°

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

∵ The measure of each exterior angle of the given polygon is 40°

∴ The number of the angles of the polygon = 360 ÷ 40 = 9

∵ The number of the angles of the polygon = the number of its sides

∴ The polygon has 9 sides