Question

what is m∠1? m∠1 = 38 ° submit

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 \(x + 35^{\circ}+110^{\circ}=180^{\circ}\).

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

\[

$$\begin{align*} x&=180^{\circ}-(35^{\circ} + 110^{\circ})\\ x&=180^{\circ}-145^{\circ}\\ x& = 35^{\circ} \end{align*}$$

\]

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 \(m\angle1=180^{\circ}-x\).

Step4: Calculate \(m\angle1\)

Substitute \(x = 35^{\circ}\) into the equation: \(m\angle1=180^{\circ}-35^{\circ}=145^{\circ}\)

Answer:

\(145^{\circ}\)