Question

question 4 of 7
in △abc, ∠a and ∠c are congruent, and the measure of ∠b is 143.6°. what is the measure of ∠a?
options: 18.2°, 36.4°, 71.8°, 143.6°

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: Use congruent angles

Given \(\angle A\cong\angle C\), so \(\angle A=\angle C\). Let \(\angle A = x\), then \(\angle C = x\).

Step3: Substitute values

We know \(\angle B = 143.6^\circ\), so substitute into the angle - sum formula: \(x + 143.6^\circ+x=180^\circ\).
Combine like terms: \(2x+143.6^\circ = 180^\circ\).
Subtract \(143.6^\circ\) from both sides: \(2x=180^\circ - 143.6^\circ=36.4^\circ\).
Divide both sides by 2: \(x=\frac{36.4^\circ}{2} = 18.2^\circ\).

Answer:

\(18.2^\circ\) (corresponding to the option "18.2°")