Question

Find the measures of the numbered angles in the diagram.

Short answer

The measure of the numbered angles is $m\angle 1=90°$, $m\angle 2=115°$, and $m\angle 3=65°$.

Step-by-step solution

Step 1. Given Information.

The provided figure is

The provided angle has the measure $115°$.

Step 2. Definition of consecutive interior angles.

When two lines are crossed by another line, it is known as transversal.The angles internal to the two parallel lines, on the same side of thetransversalare called consecutive interior angles. The sum of two consecutive interior angles is $180°$.

Step 3. Find the measure of angle 3.

The sum of the linear paired angles is $180°$, $115°+m\angle 3=180°$.

The measure of $\angle 3$ will be,

$\begin{array}{c}{115}^{\circ }+m\angle 3={180}^{\circ }\\ m\angle 3={180}^{\circ }-{115}^{\circ }\\ m\angle 3={65}^{\circ }\end{array}$

Step 4. Find the measure of angle 1.

The sum of consecutive interior angles is $180°$.

The measure of $\angle 1$ will be,

$\begin{array}{c}{90}^{\circ }+m\angle 1={180}^{\circ }\\ m\angle 1={180}^{\circ }-{90}^{\circ }\\ m\angle 1={90}^{\circ }\end{array}$

Step 5. Find the measure of angle 2.

The sum of consecutive interior angles is\[180{}^\circ \].

The measure of $\angle 2$ will be,

$\begin{array}{c}m\angle 2+m\angle 3={180}^{\circ }\\ m\angle 2={180}^{\circ }-m\angle 3\\ m\angle 2={180}^{\circ }-{65}^{\circ }\\ m\angle 2={115}^{\circ }\end{array}$

Step 6. Conclusion.

The measure of the numbered angles is $m\angle 1=90°$, $m\angle 2=115°$, and $m\angle 3=65°$.