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Question
Find the value of each angle of an octagon if four of its angles are equal and the other four are each greater than these by 20°.
Solution
An octagon has 8 sides, hence eight angles.
Sum of interior angles
= (n - 2) x 180°
= (8 - 2) x 180°
= 6 x 180°
= 1080°
Given four of its angles are equal.
Let each of the equal angles be x°
∴ Other four angles are = (x + 20)°
∴ x° + x° + x° + x° + (x + 20)° + (x + 20)° + (x + 20)° + (x + 20)° = 1080°
⇒ 8x° + 80° = 1080
⇒ 8x° = 1000°
∴ x° = 125°
∴ The four equal angles are 125°
The other four angles are
= 125° + 20°
= 145°.
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