Question

what is the measure of ∠a
a
(x + 16)°
(4x - 5)°
159°
163°
161°
157°

Explanation:

Step1: Set up equation

Vertical - angles are equal. So \(x + 16=4x - 5\).

Step2: Solve for x

Subtract \(x\) from both sides: \(16 = 3x-5\). Then add 5 to both sides: \(21 = 3x\). Divide both sides by 3, we get \(x = 7\).

Step3: Find measure of angle A

Substitute \(x = 7\) into either \(x + 16\) or \(4x - 5\). Using \(x + 16\), we have \(7+16=23^{\circ}\). But we want the non - adjacent angle. The non - adjacent angle to the one we just found and \(\angle A\) is supplementary to the angle we calculated. The sum of supplementary angles is \(180^{\circ}\). So \(\angle A=180 - 23=157^{\circ}\).

Answer:

\(157^{\circ}\)