Question 488237
the sum of 2 acute angles is 110.
the supplement of the smaller angle is 15 times the complement of the larger angle.
what is the measure of the 2 acute angles.
let the smaller angle be equal to x.
let the larger angle be equal to y.
you have:
x + y = 110
the supplement of the smaller angle is 180 - x.
the complement of the larger angle is 90 - y.
since the supplement of the smaller angle is 15 times the complement of the larger angle, you also have:
(180-x) = 15 * (90-y)
the 2 equations that you have to solve simultaneously are:
x + y = 110 (first equation)
(180-x) = 15 * (90-y) (second equation)
we'll solve by substitution.
from the first equation, you can solve for y to get:
y = 110 - x
substitute for y in the second equation to get:
(180-x) = 15 * (90 - (110-x))
remove parentheses to get:
180 - x = 15 * (-20 + x) which becomes:
180 - x = -300 + 15x
add 300 to both sides of this equation and add x to both sides of this equation to get:
180 + 300 = 15x + x
combine like terms to get:
480 = 16x
divide both sides of this equation by 16 to get:
x = 30
your original equations are:
x + y = 110 (first equation)
(180-x) = 15 * (90-y) (second equation)
substitute for x in the first equation to get:
x + y = 110 becomes:
30 + y = 110
solve for y to get:
y = 80
your values for x and y are:
x = 30
y = 80
to see if these values are good, substitute for x and y in the second equation to get:
(180-x) = 15 * (90-y) becomes:
(180-30) = 15 * (90-80) which becomes:
150 = 15 * (10) which becomes:
150 = 150
this confirms the values for x and y are good.
x is the smaller angle.
y is the larger angle.
the answer to your question is:
the smaller angle is equal to 30 degrees.
the larger angle is equal to 80 degrees.