Question

in triangle abc, the measure of angle a is 23° and the measure of angle b is 48°. what is the measure of angle c?

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So, \(A + B + C=180^{\circ}\).

Step2: Solve for angle C

We know \(A = 23^{\circ}\) and \(B = 48^{\circ}\). Then \(C=180^{\circ}-A - B\). Substitute the values of \(A\) and \(B\): \(C = 180^{\circ}-23^{\circ}-48^{\circ}\).
\[

$$\begin{align*} C&=180-(23 + 48)\\ &=180 - 71\\ &=109^{\circ} \end{align*}$$

\]

Answer:

\(109^{\circ}\)