Question

find the measure of angle b. 41)

Explanation:

Step1: Recall the triangle angle - sum formula

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(A = 32^{\circ}\), \(B=b\), and \(C = 74^{\circ}\). Then \(A + B+C=180^{\circ}\).

Step2: Solve for \(b\)

Substitute the known values into the formula: \(b+32^{\circ}+74^{\circ}=180^{\circ}\).
First, add \(32^{\circ}\) and \(74^{\circ}\): \(32^{\circ}+74^{\circ}=106^{\circ}\).
Then, \(b = 180^{\circ}-106^{\circ}\).
\(b = 74^{\circ}\).

Answer:

\(74^{\circ}\)