Question

Two angles are complementary. One angle measures 22 degree more than the other angle. Find the measure of the larger angle

Answer 1

Answer:

$\theta = 56$

Step-by-step explanation:

Represent the angles with $\theta$ and $\alpha$

Such that:

$\theta = 22 + \alpha$

Since both angles are complementary, we have:

$\theta + \alpha = 90$

Substitute $\theta = 22 + \alpha$

$22 + \alpha + \alpha = 90$

$22 + 2\alpha = 90$

Collect Like Terms

$2\alpha = 90 - 22$

$2\alpha = 68$

$\alpha = 68/2$

$\alpha = 34$

Recall that:

$\theta = 22 + \alpha$

$\theta = 22 + 34$

$\theta = 56$

Hence:

The larger angle is 56