Two angles are complementary. the sum of the measure of the first angle and half the second angle is 86.5 degr

two angles are complementary. the sum of the measure of the first angle and half the second angle is 86.5 degrees. find the measure of the angles

small angle___
other angle___

x = 1st angle
90-x = 2nd angle

x + (45 - x/2) = 86.5
x/2 + 45 = 86.5
x/2 = 41.5
x = 83 degrees -- 1st angle

90 - 83 = 7 degrees -- 2nd angle

Complimentary angles are two angles whose sum is 90 degrees.

Let x = the measure of one angle
Let y = the measure of the other angle

From the information given, you have two equations:
x+y=90 and x+0.5y=86.5

I'll solve through the substitution method:

x+y=90
x=90-y

x+0.5y=86.5
(90-y)+0.5y=86.5
90-0.5y=86.5
-0.5y=86.5-90
-0.5y=-3.5
y = -3.5/(-0.5)
y = 7

x+y=90
x+(7)=90
x=90-7
x=83

Answer: 7 degrees and 83 degrees

If angles "x" and "y" are complementary, then

x + y = 90

If the sum of the first angle and half the second angle is 86.5, then

x + 0.5y = 86.5

This is a system of equations. Solve for "x" in the first equation:

x = 90 - y

Now plug this value in for "x" in the second equation and solve for "y."

(90-y) + 0.5y = 86.5

3.5 = 0.5y

y = 7

Now you can plug in "7" for "y" in either of your original equations. The first one is easier, so let's use that one:

x + y = 90

x + 7 = 90

x = 83

The measure of the small angle ("y") is 7 degrees and the measure of the other angle ("x") is 83 degrees.

Let A and B represent the two complementary angles

A + B = 90 or A = 90 - B
A + B/2 = 86.5

Substitute: 90 - B + B/2 = 86.5

-B/2 = -3.5 or B = 7, so A = 83

Check these result in the original equations and the worded statements.

x+y=90°
x+y/2=86.5°
y/2=3.5
y=7°
x=83°
small angle =7°
other angle =83°