Question

In the diagram, find the measure of Angle y and Angle x.

PLEASE HELP ME!!

Answer 1

Part 1) The measure of angle x is 24°

Part 2) The measure of angle y is 66°

Explanation:

step 1

Find the measure of angle m∠IKL

we know that

m∠JKI+m∠IKL=180° ----> supplementary angles (form a linear pair)

we have

m∠JKI=48°

substitute

48°+m∠IKL=180°

m∠IKL=180°-48°=132°

step 2

Find the measure of angle x

we know that

The triangle IKL is an isosceles triangle

so

m∠KIL=m∠KLI=x

Remember that

The sum of the interior angles of a triangle must be equal to 180 degrees

m∠IKL+2x=180°

132°+2x=180°

2x=180°-132°

x=24°

step 3

In the right triangle JIL

Angles x and y are complementary

so

x+y=90°

24°+y=90°

y=90°-24°

y=66°