Two angles are complementary. The sum of the measures of first angle and half the measure of the second angle is 65°. How do you find the measures of the angles?

1 Answer
Sep 9, 2015

Answer:

The first angle measures #40^@# and the second angle measures #50^@#.

Explanation:

Two angles a re said to be complemetary angles when they add up to give an angle of #90^@#.

Let's assume that #angleX# is the first angle and #angleY# is the second angle. You know that

#X + Y = 90^@#

Moreover, you know that if you add the first angle to half of the second angle, you get an angle of #65^@#. This means that you can write

#X + 1/2 * Y = 65^@#

Use the first equation to find #X# as a function of #Y#

#X = 90 - Y#

Plug this into the second equation to find #Y#

#90-Y + 1/2 Y = 65#

#-1/2Y = 65 - 90#

#Y = 2 * 25 = color(green)(50^@)#

This means that angle #X# is

#X = 90 - (50) = color(green)(40^@)#