Question

two triangles are shown below. the measure of angle a is 40°, and the measure of angle c is 30°. what is the measure of angle b?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Set up the equation

Let the measure of angle \(B\) be \(x\). We know that \(A + B + C=180^{\circ}\), where \(A = 40^{\circ}\) and \(C = 30^{\circ}\). So, \(40^{\circ}+x + 30^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

First, simplify the left - hand side of the equation: \(40^{\circ}+30^{\circ}+x=70^{\circ}+x\). Then, we have \(70^{\circ}+x = 180^{\circ}\). Subtract \(70^{\circ}\) from both sides: \(x=180^{\circ}-70^{\circ}\).

Answer:

\(110^{\circ}\)