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

Answer:

53°.

Step-by-step 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.

$y=\dfrac{85}{5}$

$y=17$

The value of y is 17.

Now,

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

Therefore, the measure of ∠2 is 53°.