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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°

Step-by-step 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°

answer: 40.95

step-by-step explanation: