Home > Geometry > Complementary and Supplementary Angles

Two angles are complementary. The measure of the larger angle is 5 times the measure of the smaller. What are the measures of the angles?

Answer 1

Let ( x ) represent the measure of the smaller angle. Then, the measure of the larger angle is ( 5x ). Since the angles are complementary, their sum is ( 90^\circ ). Thus, we have the equation:

[ x + 5x = 90^\circ ]

Solving for ( x ), we get:

[ 6x = 90^\circ ]

[ x = \frac{90^\circ}{6} = 15^\circ ]

So, the measure of the smaller angle is ( 15^\circ ), and the measure of the larger angle is ( 5 \times 15^\circ = 75^\circ ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Avery Allen

#15˚,75˚#

Call the first angle's measurement #mangle1#.

The second angle is #5# times this, or #5(mangle1)#.

Since the two angles are complementary (have a sum of #90˚#), we can relate the two angles him as follows:

#mangle1+5(mangle1)=90#

#6(mangle1)=90#

#mangle1=15#

Since #mangle2# is #5# times this, #mangle2=15xx5=75#.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.