Question

lines m and n are parallel. find the measure of ∠a. m∠a = ?°

Explanation:

Step1: Identify the angle relationship

The given angle (51°) and ∠a are same - side interior angles with respect to the transversal cutting the parallel lines M and N.

Step2: Use the property of parallel lines

For parallel lines cut by a transversal, same - side interior angles are supplementary, which means their sum is 180°. So we can use the formula \(m\angle a+ 51^{\circ}=180^{\circ}\).

Step3: Solve for \(m\angle a\)

Subtract 51° from both sides of the equation: \(m\angle a=180^{\circ}- 51^{\circ}\)
\(m\angle a = 129^{\circ}\)

Answer:

129