Question

solve for ( mangle pqs ) if ( mangle pqr = 104^circ ) and ( mangle sqr = 56^circ ).

Explanation:

Step1: Identify angle relationship

From the diagram, \( \angle PQR = \angle PQS + \angle SQR \). So, \( m\angle PQS = m\angle PQR - m\angle SQR \).

Step2: Substitute given values

Given \( m\angle PQR = 104^\circ \) and \( m\angle SQR = 56^\circ \), substitute into the formula: \( m\angle PQS = 104^\circ - 56^\circ \).

Step3: Calculate the result

\( 104 - 56 = 48 \), so \( m\angle PQS = 48^\circ \).

Answer:

\( 48 \)