Question

Find the lettered angles.​

Answer 1

a) ∠a = 72°

∠b = 108°

b) ∠
`x` = 56°

c) ∠m = 95°

Explanation:

• Sum of interior angles of a polygon = (n − 2) × 180
  (where n is the number of sides)
  
• If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle.
  The sum of the exterior angles of a polygon = 360°
  
• The sum of angles on a straight line = 180°
  

a) This shape is a regular polygon with 5 sides.

Therefore, sum of the interior angles = (5 - 2) x 180 = 540°

Therefore, ∠b = 540 ÷ 5 = 108°

∠a = 180 - 108 = 72°

b) The sum of the exterior angles of a polygon = 360°

Therefore, 55 + 63 + 52 + 44 + 90 +
`x` = 360

304 +
`x` = 360

`x` = 360 - 304 = 56°

c) The sum of the exterior angles of a polygon = 360°

Therefore, 40 + 40 + 35 + 40 + 50 + 60 + m = 360

265 + m = 360

m = 360 - 265 = 95