Question

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Answer 1

m∠XYZ = 162°

Explanation:

We can see that ∠XYZ is an exterior angle while ∠W and ∠X are the opposite interior angles.

We know that the exterior angle of triangle is equal to the sum of opposite interior angles

Given

m∠XYZ = (15x-18)°

m∠W = (5x+2)°

m∠X = (8x+4)°

Mathematically it can be written as:

m∠X+m∠W = m∠XYZ

`8x+4+5x+2 = 15x-18\\13x+6 = 15x-18\\13x-15x = -18-6\\-2x = -24\\(-2x)/(-2) = (-24)/(-2)\\x = 12`

Putting x=12 in m∠XYZ

`15x-18\\=15(12)-18\\=180-18=162`

Hence,

m∠XYZ = 162°