Question

\angle1 and \angle2 are complementary. If \angle1 measures 2y + 3

2
y
+
3
and \angle2 measures 3y + 2
3
y
+
2
, what is the measure of \angle2?

Answer 1

53°.

Explanation:

It is given that ∠1 and ∠2 are complementary angles.

`\angle 1=2y+3\text{ and }\angle 2=3y+2`

If two angle are complementary angle, then their sum is 90°.

∠1 and ∠2 are complementary angles. So,

`\angle 1+\angle 2=90`

`(2y+3)+(3y+2)=90`

`5y+5=90`

Subtract both sides by 5.

`5y+5-5=90-5`

`5y=85`

Divide both sides by 5.

`y=(85)/(5)`

`y=17`

The value of y is 17.

Now,

`\angle 2=3y+2=3(17)+2=51+2=53`

Therefore, the measure of ∠2 is 53°.