Question

using the parallelogram angle theorem
devin started the work shown to solve for
the unknown angle measures.
devins work

1. ( 8 x - 1 + 9 x - 6 = 180 )
2. ( 17 x - 7 = 180 )
3. ( 17 x = 187 )

what are the measures of angles ( q ) and
( r )?

Explanation:

Step1: Solve for \(x\)

From \(17x = 187\), divide both sides by \(17\):
\(x=\frac{187}{17}=11\)

Step2: Find the measure of \(\angle Q\)

Substitute \(x = 11\) into \((9x - 6)^{\circ}\):
\(9x-6=9\times11 - 6=99 - 6=93^{\circ}\)

Step3: Find the measure of \(\angle R\)

Substitute \(x = 11\) into \((8x - 1)^{\circ}\):
\(8x-1=8\times11-1=88 - 1=87^{\circ}\)

Answer:

The measure of \(\angle Q\) is \(93^{\circ}\) and the measure of \(\angle R\) is \(87^{\circ}\)