Question

In Exercises 6 and 7, use the given information to find $m\angle 2$.

$\angle 1$ and $\angle 2$ arecomplementary angles, and $m\angle 1=45°$.

Short answer

The measure of angle $m\angle 2$ is $45°$.

Step-by-step solution

Step 1. Given Information.

$m\angle 1=45°$

Step 2. Concept used.

If the sum of two angles is $90°$ then the angles are called complementary angles and if the sum is $180°$ then the angles are called supplementary angles.

Step 3. Calculation.

Since $\angle 1$ and $\angle 2$ are complementary angles.

$\begin{array}{c}m\angle 1+m\angle 2=90°\\ 45°+m\angle 2=90°\\ m\angle 2=90°-45°\\ =45°\end{array}$

Step 4. Conclusion.

The measure of the angle that is complementary to an angle measuring $45°$ is $45°$.