Question

1. if mo bisects ∠pmn, m∠pmn = 74° and m∠omn = (2x + 7)°, find the value of x.

Explanation:

Step1: Recall angle bisector property

Since \( MO \) bisects \( \angle PMN \), it divides \( \angle PMN \) into two equal angles. So, \( m\angle OMN=\frac{1}{2}m\angle PMN \).

Step2: Substitute given values

We know \( m\angle PMN = 74^\circ \) and \( m\angle OMN=(2x + 7)^\circ \). Substituting into the equation from Step 1:
\( 2x+7=\frac{74}{2} \)

Step3: Simplify and solve for \( x \)

First, calculate \( \frac{74}{2}=37 \). So the equation becomes:
\( 2x + 7=37 \)
Subtract 7 from both sides:
\( 2x=37 - 7 \)
\( 2x=30 \)
Divide both sides by 2:
\( x=\frac{30}{2}=15 \)

Answer:

\( x = 15 \)