Question

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Answer 1

Answer:

x = 8

Step-by-step explanation:

m<PQR = (2x + 6)°

m<RPQ = (x - 7)°

m<QRS = (5x - 17)°

<PQR and <RPQ are interior angles opposite to the exterior angle <RPQ.

Therefore,

m<PQR + m<RPQ = m<QRS (Exterior Angle Theorem of a Triangle)

Substitute in the values

2x + 6 + x - 7 = 5x - 17

Add like terms

3x - 1 = 5x - 17

Collect like terms

3x - 5x = 1 - 17

-2x = -16

-2x/-2 = -16/-2

x = 8