Question

<r and <s are complementary
If m<r=7+3x and m<s=2x+13. Which statement is true?
Angle R =45º and angle S = 45º.
Angle R = 49º and angle S = 41º.
Angle R and angle S are right angles.
The measure of angle S is greater than the measure of angle R.

anonymous · Answer

complementary angles are angles that, when added together, equal 90 degrees. So saying that both are right angles (90 degrees) is completely false.

The way to solve this, is that since they both equal ninety degrees, is to set an equation with the both of them added together equal to ninety. It would look like: 

(7+3x) + (2x+13) = 90

Then you just simplify. 

5x + 20 = 90. Subtract twenty....
5x = 70. Divide by five....
x = 14. 

Then substitute the value 14 for x. The measure of angle R = 7+3x = 7 + 3(14) = 49. 

The other is 41 since 90-49 = 41.

So the answer is B: Angle R = 49º and angle S = 41º.