Question
Solve for m, angle, P, Q, Rm∠PQR if m, angle, P, Q, S, equals, 79, degreesm∠PQS=79
∘
and m, angle, S, Q, R, equals, 32, degreesm∠SQR=32
∘
.
∘
and m, angle, S, Q, R, equals, 32, degreesm∠SQR=32
∘
.
Answers
Answered by
GPT-4o mini
To solve for \( m \angle PQR \), we can use the information given about the angles in triangle PQR.
We know:
- \( m \angle PQS = 79^\circ \)
- \( m \angle SQR = 32^\circ \)
To find \( m \angle PQR \), we can use the fact that the sum of angles in triangle PQS is \( 180^\circ \):
\[
m \angle PQS + m \angle SQR + m \angle PQR = 180^\circ
\]
Substituting the known values into the equation:
\[
79^\circ + 32^\circ + m \angle PQR = 180^\circ
\]
Now, adding the angles on the left side:
\[
111^\circ + m \angle PQR = 180^\circ
\]
Next, we will isolate \( m \angle PQR \):
\[
m \angle PQR = 180^\circ - 111^\circ
\]
\[
m \angle PQR = 69^\circ
\]
Thus, the measure of angle \( PQR \) is \( \boxed{69^\circ} \).
We know:
- \( m \angle PQS = 79^\circ \)
- \( m \angle SQR = 32^\circ \)
To find \( m \angle PQR \), we can use the fact that the sum of angles in triangle PQS is \( 180^\circ \):
\[
m \angle PQS + m \angle SQR + m \angle PQR = 180^\circ
\]
Substituting the known values into the equation:
\[
79^\circ + 32^\circ + m \angle PQR = 180^\circ
\]
Now, adding the angles on the left side:
\[
111^\circ + m \angle PQR = 180^\circ
\]
Next, we will isolate \( m \angle PQR \):
\[
m \angle PQR = 180^\circ - 111^\circ
\]
\[
m \angle PQR = 69^\circ
\]
Thus, the measure of angle \( PQR \) is \( \boxed{69^\circ} \).