Question

Triangle XYZ is isosceles with <Z as the vertex angle. 

If <X = 5x+33, <Y = 33x+42,

 Find <Z

Answer 1

Answer: ∠Z = 117.2°

Explanation:

∠X and ∠Y are isosceles so they are congruent (equal to each other)

5x + 33 = 33x + 42

-5x -5x

33 = 28x + 42

-42 -42

-9 = 28x

`(-9)/(28) = (28x)/(28)`

`-(9)/(28) = x`

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∠X + ∠Y + ∠Z = 180° Triangle angle sum theorem

5x + 33 + 33x + 42 + ∠Z = 180°

38x + 75 + ∠Z = 180°

-75 -75

38x + ∠Z = 105°

38
`(-(9)/(28))` + ∠Z = 105°

-12.2 + ∠Z = 105°

+12.2 +12.2

∠Z = 117.2°