Question

use the figure. find the measures of ∠a and ∠b.
the measure of ∠a is
the measure of ∠b is

Explanation:

Step1: Recall Triangle Angle Sum

The sum of angles in a triangle is \(180^\circ\). So, \(\angle A + \angle B + \angle C = 180^\circ\).

Step2: Substitute Known Values

Given \(\angle A = x\), \(\angle B = x + 20\), \(\angle C = 40^\circ\). Substitute into the formula: \(x + (x + 20) + 40 = 180\).

Step3: Solve for \(x\)

Simplify the equation: \(2x + 60 = 180\). Subtract 60: \(2x = 120\). Divide by 2: \(x = 60\).

Step4: Find \(\angle A\) and \(\angle B\)

\(\angle A = x = 60^\circ\). \(\angle B = x + 20 = 60 + 20 = 80^\circ\).

Answer:

The measure of \(\angle A\) is \(60^\circ\).
The measure of \(\angle B\) is \(80^\circ\).