Question

on quiz triangle angle sum and congruency
find the measure of ∠a in the triangle below.

Explanation:

Step1: Use triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 37)+(x + 67)+90=180\).

Step2: Simplify the equation

Combine like terms: \(2x+37 + 67+90=180\), \(2x+194 = 180\).

Step3: Solve for \(x\)

Subtract \(194\) from both sides: \(2x=180 - 194=-14\), then \(x=-7\).

Step4: Find \(m\angle A\)

Substitute \(x = - 7\) into \(x + 37\). So, \(m\angle A=-7+37\).

Answer:

\(30^{\circ}\)