Question

First solve for x, then find ∡RQW. ∡WQP=139+x, ∡RQW=31+x & ∡RQP=152°

Answer 1

`x = -9`

`RQW = 22`

Explanation:

Given

`WQP = 139 + x`

`RQW = 31 + x`

`RQP = 152`

Required

Determine x and WQP

From the attachment;

`RQP = RQW + WQP`

Substitute 152 for RQP, 31 + x for RQW, 139 + x for WQP

`152 = 31 + x + 139 + x`

Collect Like Terms

`152 - 31 - 139 = x + x`

`-18 = 2x`

Divide both sides by 2

`(-18)/(2) = x`

`x = -9`

To solve for RQW; substitute -9 for x in RQW = 31 + x

`RQW = 31 + (-9)`

`RQW = 31 -9`

`RQW = 22`