Question

Complete each sentence with the most appropriate word, phase or value.

If $\angle \mathbf{1}$ and $\angle \mathbf{2}$ are complements and $\text{m}\angle \mathbf{1}=\mathbf{74}$, then$\text{m}\angle \mathbf{2}=$ ________.

Short answer

The answer is 16 .

Step-by-step solution

- Define complementary angles. 

Two angles are said to be complementary if their sum is equal to ${90}^{\circ }$.

- State the explanation.

The sum of complementary angles is ${90}^{\circ }$.

Then,

$\begin{array}{c}\angle 1+\angle 2=90\\ 74+\angle 2=90\\ \angle 2=90-74\\ \angle 2={16}^{\circ }\end{array}$

Hence, the blank is filled by ${16}^{\circ }$.

- State the conclusion.

Therefore,“If $\angle 1$ and $\angle 1$ are complements and $m\angle 1=74$, then $m\angle 2=$16”.