Question

using algebra to solve for missing measures 10. if ( mangle pqt = 3x + 47 ) and ( mangle sqr = 6x - 25 ), find the measure of ( angle sqr ).

Explanation:

Step1: Identify vertical angles

Vertical angles are equal, so \( m\angle PQT = m\angle SQR \).
\( 3x + 47 = 6x - 25 \)

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\( 47 = 3x - 25 \)
Add 25 to both sides:
\( 72 = 3x \)
Divide by 3:
\( x = 24 \)

Step3: Find \( m\angle SQR \)

Substitute \( x = 24 \) into \( 6x - 25 \):
\( 6(24) - 25 = 144 - 25 = 119 \)

Answer:

The measure of \( \angle SQR \) is \( 119^\circ \).