Question

find ( mangle a ).
( mangle a=)____

Explanation:

Step1: Use the property of adjacent angles on a straight line

Since \((3x + 5)^{\circ}\) and \((2x-15)^{\circ}\) are adjacent angles on a straight line, their sum is \(180^{\circ}\).

$$
LATEXBLOCK0
$$

Step2: Solve for \(x\)

Add \(10\) to both sides of the equation \(5x - 10=180\):

$$
LATEXBLOCK1
$$

Divide both sides by \(5\):

$$ x=\frac{190}{5}=38 $$

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

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

$$ 3x+5=3\times38 + 5=114 + 5=119 $$

Step4: Use the property of supplementary angles

Since \(\angle A\) and the angle \((3x + 5)^{\circ}\) are supplementary (they form a linear pair), \(m\angle A=180-(3x + 5)\)
Substitute \(x = 38\) into \(180-(3x + 5)\):

$$
LATEXBLOCK2
$$

Another way:
Since \(\angle A\) and \((2x-15)\) are vertical angles. First, substitute \(x = 38\) into \((2x-15)\)

$$ 2x-15=2\times38-15=76-15 = 61 $$

Answer:

\(61^{\circ}\)