Question

If m PQS=16, M SQR=(9x+17),and m PQR=(12x-6) find m PQR Please answer with work

Answer 1

Answer:

$\angle PQR=30^{\circ}$

Step-by-step explanation:

It is given that,

$\angle PQS=16^{\circ}\\\\\angle SQR=(9x+17)^{\circ}\\\\\angle PQR=(12x-6)^{\circ}$

We need to find the measure of $\angle PQR$.

From the given figure, $\angle PQR=\angle PQS+\angle SQR$

Putting all the values, we get :

$12x-6=16+9x+17\\\\12x-9x=16+17+6\\\\3x=39\\\\x=13$

$\angle PQR=12x-6\\\\=12(3)-6\\\\=30^{\circ}$

So, the measure of $\angle PQR$ is 30 degrees.