Answer:
a) ∠a = 72°
∠b = 108°
b) ∠[tex]x[/tex] = 56°
c) ∠m = 95°
Step-by-step 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 + [tex]x[/tex] = 360
304 + [tex]x[/tex] = 360
[tex]x[/tex] = 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
