Question

question 4 (multiple choice worth 2 points) interior and exterior angles 1.0 one interior angle of a triangle is 95.5°, and the other two interior angles are congruent. what is the degree measure of one of the congruent angles? 42.25° 47.75° 84.5° 90°

Explanation:

Step1: Recall the sum of interior angles of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the measure of each of the congruent angles be \(x\). We know one angle is \(95.5^{\circ}\), so the equation is \(95.5 + x + x=180\).

Step2: Simplify the equation

Combine like - terms: \(95.5+2x = 180\). Then, subtract \(95.5\) from both sides: \(2x=180 - 95.5\). So, \(2x = 84.5\).

Step3: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{84.5}{2}=42.25\).

Answer:

\(42.25^{\circ}\)