2. the sum of the measures of angle x and angle yis 90. if the measure of angle xis 30 less than twice the
measure of angle y, what is the measure of angle x?
o 20°
o 35°
50°
65°

50 degrees

Step-by-step explanation:

x + y = 90

x = 2y - 30

2y - 30 + y = 90

3y - 30 = 90

3y = 90 + 30

3y = 120

y = 120/3

y = 40

x = 2y - 30

x = 2(40) - 30

x = 80 - 30

x = 50 < angle x

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen