Question

angle RIO and angle RIE are supplementary one angle measures three times the other angle what is the complement of the smaller angle

Answer 1

The complement of the smaller angle is 45 degrees

Explanation:

Let

x -----> the measure of one angle (m∠RIO)

y -----> the measure of the other angle (m∠RIE)

we know that

If two angles are supplementary, then their sum is equal to 180 degrees

so

x+y=180 -----> equation A

x=3y -----> equation B

substitute equation B in equation A and solve for y

3y+y=180

4y=180

y=45°

Find the value of x

x=3(45)=135°

therefore

m∠RIO=135°

m∠RIE=45° ------> smaller angle

Remember that

If two angles are complementary, then their sum is equal to 90 degrees

therefore

The complement of the smaller angle (m∠RIE=45°) is 45 degrees