Question

When angles are complementary, the sum of their measures is 90 degrees. Two complementary angles have measures 2x - 10 degrees and 3x - 10 degrees. Find the measures of each angle.

Answer 1

2x - 10 + 3x - 10 = 90
5x - 20 = 90
5x = 90 + 20
5x = 110
x = 110/5
x = 22

one angle is 2x - 10 = 2(22) - 10 = 44 - 10 = 34 degrees
one angle is 3x - 10 = 3(22) - 10 = 66 - 10 = 56 degrees

Answer 2

Answer: The measures of the two angles are 34° and 56°.

Step-by-step explanation: Given that when angles are complementary, the sum of their measures is 90 degrees.

Two complementary angles have measures 2x - 10 degrees and 3x - 10 degrees.

We are to find the measure of each of the two angles.

According to the given information, we have

`(2x-10)^\circ+(3x-10)^\circ=90^\circ\\\\\Rightarrow 2x-10+3x-10=90\\\\\Rightarrow 5x-20=90\\\\\Rightarrow 5x=90+20\\\\\Rightarrow 5x=110\\\\\Rightarrow x=(110)/(5)\\\\\Rightarrow x=22.`

Therefore, the measures of the two angles are

`(2*22-10)^\circ=(44-10)^\circ=34^\circ`

and

`(3*22-10)^\circ=(66-10)^\circ=56^\circ.`

Thus, the measures of the two angles are 34° and 56°.