Two complementary angles have measures of 2x+5° and 3x-10°. What is the measure of each of the angles?

2 Answers
Nov 9, 2016

2x + 5 = 43^@
3x - 10 = 47^@

Explanation:

A complementary angles means angles that add up to 90 degrees. The two angles given in the question are complementary angles.
So
Our first angle (2x+5) plus the second angle (3x-10) is equal to 90 degrees
(2x+5) + (3x-10) = 90
Now we solve for x, first we add up the like terms
2x + 3x + 5 - 10 = 90
5x - 5 = 90
Add 5 to both sides
5x = 95
Divide both sides by 5 we get
x = 19
Now and after we find x we substitute it to get our two angles
2x + 5 = 2(19) + 5 = 43^@
3x - 10 = 3 (19) - 10 = 47^@
Hope it helps :)

Nov 9, 2016

43^@" and " 47^@

Explanation:

Complementary angles are color(blue)"2 angles whose sum is 90 degrees"

Hence 2x + 5 and 3x - 10 , sum to 90.

rArr2x+5+3x-10=90larr" equation to be solved"

rArr5x-5=90

add 5 to both sides of the equation.

5xcancel(-5)cancel(+5)=90+5

rArr5x=95

To solve for x, divide both sides by 5.

(cancel(5) x)/cancel(5)=95/5

rArrx=19" is the solution"

The 2 angles are therefore.

2x+5=(2xx19)+5=43^@

and 3x-10=(3xx19)-10=47^@