Question

what is m∠1? m∠1 =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(x\). So, \(x+48^{\circ}+78^{\circ}=180^{\circ}\).

Step2: Solve for the third - interior angle \(x\)

\[

$$\begin{align*} x&=180^{\circ}-(48^{\circ} + 78^{\circ})\\ x&=180^{\circ}-126^{\circ}\\ x& = 54^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

\(\angle1\) and the third - interior angle \(x\) form a linear pair. A linear pair of angles sums to 180°. So, \(m\angle1+x = 180^{\circ}\). Since \(x = 54^{\circ}\), then \(m\angle1=180^{\circ}-54^{\circ}\).

Step4: Calculate \(m\angle1\)

\(m\angle1 = 126^{\circ}\)

Answer:

\(126\)