SOLUTION: One acute angle of a right triangle is 36 degrees more than twice the other angle write an equation that can be used to find the measure of the smaller angle

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Question 1061383: One acute angle of a right triangle is 36 degrees more than twice the other angle write an equation that can be used to find the measure of the smaller angle
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let y be the smaller angle.
let x be the larger angle.

first equation is x = 2y + 36
second equation is x + y = 90

solve these two euations simultaneously and you get the answer you need.

x + y = 90 because these are two acute angles of a right triangle.

x = 2y + 36 because the larger angle is 36 more than 2 times the smaller angle.

replace x in the second equation by 2y + 36 from the first equation to get:

2y + 36 + y = 90

combine like terms to get 3y + 36 = 90

subtract 36 from both sides of this equation to get 3y = 90 - 36

simplify to get 3y = 54.

solve for y to get y = 18.

the larger angles is twice this plus 36 which makes the larger angle equal to 72 degrees.

18 + 72 = 90 degrees which confirms the solution is good.

the solution is that the smaller angle is equal to 18 degrees.