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 <u>x, y, and two vertices of the polygon</u>
∵ 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°
<em>The sum of the measures of the </em><em>interior angle and the exterior angle</em><em> at any vertex of the polygon is </em><em>180°</em>
∵ 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°
<em>The </em><em>sum </em><em>of the measures of the </em><em>exterior angles</em><em> of any polygon is </em><em>360°</em>
∵ 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
