The angles of a polygon are x, 2x, 2x, (x + 30^{}), (x + 20^{}) and (x - 10^{}). Find the value of x

Correct Answer is : 85∘85^{}85∘

Correct Answer is : 85∘85^{}85∘

Test Index

WAEC Mathematics 2018 Paper

Question : 15

Total: 50

30^{\circ}

20^{\circ}

10^{\circ}

). Find the value of x

Solution:

Concept:

The sum of interior angles of a polygon with

n

sides is

(n - 2) \times 180^\circ

Explanation:

The polygon has 6 angles, so

n = 6

Sum of interior angles

= (6 - 2) \times 180^\circ = 720^\circ

Write the sum of the given angles:

x + 2x + 2x + (x + 30^\circ) + (x + 20^\circ) + (x - 10^\circ) = 720^\circ

Combine like terms:

8x + 40^\circ = 720^\circ

Subtract

40^\circ

from both sides:

8x = 680^\circ

Divide both sides by 8:

x = 85^\circ

Answer:

x = 85^\circ

Correct option: D.

85^\circ

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