Question

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Answer 1

According to the above problem

`(7x) + (11x - 5) + 41 = 180 \\ 18x = 180 + 5 - 41 \\ 18x = 144 \\ \boxed{x = 8}`

Therefore, the angles are 41°, 56° and 83°.

Answer 2

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Answer:

• x = 8
• 7x = 56
• 11x -5 = 83

Explanation:

Consecutive interior angles have a sum of 180°, so ...

(41 +7x) +(11x -5) = 180

18x +36 = 180 . . . . . . . . . simplify

x + 2 = 10 . . . . . . . . . . . . divide by 18

x = 8

The angle 7x is then ...

7x = 7(8) = 56 . . . . degrees

The angle 11x -5 is ...

11x -5 = 11(8) -5 = 83 . . . . degrees

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Check

41 + 56 + 83 = 97 +83 = 180 . . . . as required