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 \(x + 43^{\circ}+46^{\circ}=180^{\circ}\).

Step2: Calculate the third - interior angle

\[

$$\begin{align*} x&=180^{\circ}-(43^{\circ} + 46^{\circ})\\ x&=180^{\circ}-89^{\circ}\\ x& = 91^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

\(\angle1\) and the third - interior angle of the triangle form a linear pair. A linear pair of angles sums to 180°. Let \(m\angle1=y\). Then \(y + 91^{\circ}=180^{\circ}\).

Step4: Solve for \(m\angle1\)

\[

$$\begin{align*} y&=180^{\circ}-91^{\circ}\\ y&=89^{\circ} \end{align*}$$

\]

Answer:

89