# Two angles are complementary. The larger angle is 16 degrees larger than the smaller angle. Find the measure of both angles?

Mar 8, 2018

color(brown)(hat A = 53^@, hat B = 37^@

#### Explanation:

Two angles are said to be complementary, if their sum equals ${90}^{\circ}$

Let the two angles be $\hat{A} , \hat{B}$

Given $\hat{A} + \hat{B} = {90}^{\circ}$ Eqn (1)

Also given $\hat{A} = \hat{B} + 16$

Substituting value of $\hat{A}$ in terms of $\hat{B}$ in Eqn (1),

$\left(\hat{B} + 16\right) + \hat{B} = 90$

$2 \hat{B} = 90 - 16 74$

hat B = 74 / 2 = color (brown)(37^@

Substituting value of $\hat{B}$ in Eqn (1),

hat A = 90 - 37 = color(brown)(53^@