Question

angle pqr is a right angle. the measure of angle sqr is 40°. the measure of angle pqs is x°. what is the value of x? x = 50

Explanation:

Step1: Identify the right angle

Angle \( PQR \) is a right angle, so \( \angle PQR = 90^\circ \).

Step2: Use angle addition postulate

We know that \( \angle PQR=\angle PQS + \angle SQR \). Given \( \angle SQR = 40^\circ \) and \( \angle PQS=x^\circ \), we substitute into the equation: \( 90^\circ=x^\circ + 40^\circ \).

Step3: Solve for \( x \)

Subtract \( 40^\circ \) from both sides of the equation: \( x = 90 - 40 \).
\( x = 50 \)

Answer:

\( x = 50 \)