Question

what is m∠1? m∠1 = (square^{circ})

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(x\). So \(x + 69^{\circ}+72^{\circ}=180^{\circ}\).

Step2: Calculate the third - interior angle

\[

$$\begin{align*} x&=180^{\circ}-(69^{\circ} + 72^{\circ})\\ x&=180^{\circ}-141^{\circ}\\ x& = 39^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

\(\angle1\) and the third - interior angle \(x\) form a linear pair. A linear pair of angles is supplementary, i.e., their sum is 180°. So \(m\angle1+x = 180^{\circ}\).

Step4: Calculate \(m\angle1\)

\[

$$\begin{align*} m\angle1&=180^{\circ}-x\\ m\angle1&=180^{\circ}-39^{\circ}\\ m\angle1&=141^{\circ} \end{align*}$$

\]

Answer:

141