Question

find the measure of angle a.
23)

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). In a right - angled triangle (one angle is \(90^{\circ}\)), we have \(3x + 6x+90^{\circ}=180^{\circ}\).

Step2: Solve the equation for \(x\)

Combine like terms: \(9x+90^{\circ}=180^{\circ}\).
Subtract \(90^{\circ}\) from both sides: \(9x=180^{\circ}-90^{\circ}=90^{\circ}\).
Divide both sides by \(9\): \(x = 10^{\circ}\).

Step3: Find the measure of angle \(A\)

Since angle \(A = 3x\), substitute \(x = 10^{\circ}\) into \(3x\). Then angle \(A=3\times10^{\circ}=30^{\circ}\).

Answer:

\(30^{\circ}\)