Answer:
6. The value of a = 18
7. The value of c = 72
8. a = 15 , b = 30 , c = 10
9. The sum = 900°
10. The measure = 164.3°
Explanation:
In number 6.
∵ The figure is regular decagon (all sides are equal
∴ The measure of each vertex angle = [(10 - 2) × 180] ÷ 10 = 144°
∵ The triangle which contains a is isosceles Δ
∴ a = (180 - 144) ÷ 2 = 18°
In number 7.
∵ The figure which contains a and b is regular pentagon
∴ The measure of each vertex angle = [(5 - 2) × 180] ÷ 5 = 108
∵ c is an exterior angle to the regular polygon
∴ c = 180 - 108 = 72°
In number 8.
∵ The two lines are parallel and intersected by a transversal
∴ b = 3c ⇒ corresponding angles
∵ 3c + 5b = 180 ⇒ straight angle
∴ b + 5b = 180 ⇒ 6b = 180
∴ b = 180 ÷ 6 = 30
∵ b = 3c ⇒ ∴ 3c = 30
∴ c = 30 ÷ 3 = 10
∵ b = 2a ⇒ vertically opposite angles
∴ 2a = 30 ⇒ a = 30 ÷ 2 = 15
9. The sum of the interior angles of any polygon = (n - 2) × 180
where n is the number of sides
The sum = (7 - 2) × 180 = 900°
10. The m of each interior angle of a regular polygon = [(n - 2) × 180] ÷ n
∴ The measure = [(23 - 2) × 180] ÷ 23 = 164.3°