Question

question 2 (5 points)
listen
in the given figure, if ( mangle pqs = mangle tqr = 30^{circ} ) and ( mangle pqr = 85^{circ} ), find ( mangle sqt ).
a) ( 55^{circ} )
b) ( 25^{circ} )
c) ( 115^{circ} )
d) ( 60^{circ} )

Explanation:

Step1: Analyze angle composition

We know that \( \angle PQR=\angle PQS + \angle SQT+\angle TQR \). Given \( \angle PQS = 30^{\circ} \), \( \angle TQR = 30^{\circ} \) and \( \angle PQR=85^{\circ} \).

Step2: Solve for \( \angle SQT \)

Substitute the known values into the equation: \( 85^{\circ}=30^{\circ}+\angle SQT + 30^{\circ} \).
First, simplify the right - hand side: \( 30^{\circ}+30^{\circ}=60^{\circ} \), so the equation becomes \( 85^{\circ}=60^{\circ}+\angle SQT \).
Then, solve for \( \angle SQT \) by subtracting \( 60^{\circ} \) from both sides: \( \angle SQT=85^{\circ}- 60^{\circ}=25^{\circ} \).

Answer:

B) \( 25^{\circ} \)