Question

Two angles,
∠
X
and
∠
Y
, are complementary. The measure of
∠
X
is 12 degrees greater than the measure of
∠
Y
. What is the measure of
∠
X
?


39 degrees


45 degrees


51 degrees


96 degrees

Answer 1

Let Y = measure of ∠Y. Then X = Y + 12 and X + Y = 90 (complements).

So (Y + 12) + Y = 90 → 2Y + 12 = 90 → 2Y = 78 → Y = 39.

Thus X = Y + 12 = 39 + 12 = 51 degrees.

Answer: 51 degrees.