Question

find the measure of the missing angle. show all of your work.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Set up an equation for the first triangle

Let the missing angle be \(x\). For the first triangle with angles \(53^{\circ}\), \(46^{\circ}\), and \(x\), we have \(x + 53^{\circ}+46^{\circ}=180^{\circ}\).

Step3: Solve for \(x\) in the first triangle

\[

$$\begin{align*} x&=180^{\circ}-(53^{\circ} + 46^{\circ})\\ x&=180^{\circ}-99^{\circ}\\ x& = 81^{\circ} \end{align*}$$

\]

Step4: Set up an equation for the second triangle

For the second triangle with angles \(50^{\circ}\), \(53^{\circ}\), and \(x\), we have \(x+50^{\circ}+53^{\circ}=180^{\circ}\).

Step5: Solve for \(x\) in the second triangle

\[

$$\begin{align*} x&=180^{\circ}-(50^{\circ}+53^{\circ})\\ x&=180^{\circ}-103^{\circ}\\ x&=77^{\circ} \end{align*}$$

\]

Answer:

For the first triangle, the missing - angle measure is \(81^{\circ}\). For the second triangle, the missing - angle measure is \(77^{\circ}\).