Question

find ( m angle a ).

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\). So, \((3x + 5)+(2x - 15)=180\)

Step2: Solve the equation for \(x\)

Combine like terms: \(3x+2x+5 - 15=180\), which simplifies to \(5x-10 = 180\).
Add \(10\) to both sides: \(5x=180 + 10=190\).
Divide both sides by \(5\): \(x=\frac{190}{5}=38\)

Step3: Find the measure of one of the non - angle \(A\) angles

Substitute \(x = 38\) into \(3x + 5\): \(3\times38+5=114 + 5=119\)

Step4: Use the property of vertical angles (or linear pair with angle \(A\))

Angle \(A\) and the angle \((3x + 5)\) are supplementary (linear pair). So \(m\angle A=180-(3x + 5)\)
Since \(3x + 5 = 119\), then \(m\angle A=180-119 = 61\)

Answer:

\(61^{\circ}\)