Question

1. if (overline{mo}) bisects (angle pmn), (mangle pmn = 74^circ) and (mangle omn = (2x + 7)^circ), find the value of (x).

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, \( m\angle OMN=\frac{1}{2}m\angle PMN \).
Given \( m\angle PMN = 74^\circ \) and \( m\angle OMN=(2x + 7)^\circ \), we substitute into the formula:
\( 2x + 7=\frac{74}{2} \)

Step2: Simplify the Right - Hand Side

Calculate \( \frac{74}{2}=37 \), so the equation becomes:
\( 2x + 7 = 37 \)

Step3: Solve for x

Subtract 7 from both sides:
\( 2x=37 - 7 \)
\( 2x = 30 \)
Divide both sides by 2:
\( x=\frac{30}{2}=15 \)

Answer:

\( x = 15 \)