Answer:
Part 1) The measure of angle x is 24°
Part 2) The measure of angle y is 66°
Step-by-step 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°
