Answer:
x = 33
y = 66
m<BGK = 71°
Explanation:
✔️(2x + 5) + (3x + 10) = 180° (consecutive interior angles)
Solve for x
2x + 5 + 3x + 10 = 180
Add like terms
5x + 15 = 180
5x = 180 - 15 (subtraction property of equality)
5x = 165
Divide both sides by 5
x = 33
✔️(2x + 5) = (y + 5) (alternate interior angles are congruent)
Plug in the value of x
2(33) + 5 = y + 5
66 + 5 = y + 5
71 = y + 5
71 - 5 = y
66 = y
y = 66
✔️m<BGK = (y + 5) (vertical angles)
Plug in the value of y
m<BGK = (66 + 5)
m<BGK = 71°