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Question

Two angles are complementary if their sum is 90 deg. If you have two complementary angles and the 1st angle is 10 deg smaller than four times the measure of the 2nd angle. Find the angles.

Answer 1

We have a problem with 2 unknowns, so we must have 2 equations to solve it.

Let x=1st angle

     y=2nd angle

Eq. I:    x+y=90

Eq. II:   x=4y-10

Using the substitution method, substitute x from Eq. II into Eq. I and solve for y.

            x+y=90                  Eq. I

           (4y-10)+y=90          substitute for x from Eq. I

           4y+y=90+10           combine like terms by adding 10 to both sides

           5y=100                   simplify

           y=100/5                 divide both sides by 5 to isolate y

           y=20                      answer for y

Using this value for y in Eq. I we can now solve for x.

           x+y=90                  Eq. I

           x+20=90                substitute value for y from above

           x=90-20                 subtract 20 from both sides

           x=70

Therefore, the 1st angle is 70⁰ and the 2nd angle is 20⁰.

Answer 2

x +y = 90

x = 4y - 10

Substitute:

4y - 10 + y = 90

5y = 100

y = 20

x = 70