Question

One of two complementary angles is 35º larger than the other. What is the measure of both angles?​

Answer 1

Given:

One of two complementary angles is 35º larger than the other.

To find:

The measure of both angles.

Solution:

Let x degrees be the measure of smaller angle. Then the measure of larger angle is:

$\text{Larger angle}=(x+35)^\circ$

We know that the sum of complimentary angles is always 90 degrees. So,

$x^\circ+(x+35)^\circ=90^\circ$

$(2x+35)^\circ=90^\circ$

$2x+35=90$

Subtract 35 from both sides.

$2x=90-35$

$2x=55$

$x=\dfrac{55}{2}$

$x=27.5$

The measure of smaller angle is 27.5 degrees.

Now, the measure of larger angle is:

$\text{Larger angle}=(27.5+35)^\circ$

$\text{Larger angle}=62.5^\circ$

Therefore, the measures of both angles are 27.5° and 62.5°.