Answer:
x = 20,
y = 15
m<1 = 75°
m<2 = 75°
m<3 = 75°
m<4 = 105°
Step-by-step explanation:
m<1 = 3x + 15
m<2 = 4x - 5
m<3 = 5y
✔️m<1 = m<2 (corresponding angles are congruent)
3x + 15 = 4x - 5 (substitution)
Collect like terms
3x - 4x = -15 - 5
-x = -20
Divide both sides by -1
x = 20
✔️m<3 = m<2 (corresponding angles are congruent)
5y = 4x - 5 (substitution)
Plug in the value of x and solve for y
5y = 4(20) - 5
5y = 80 - 5
5y = 75
5y/5 = 75/5
y = 15
✔️Find the measure of each labelled angle:
x = 20, y = 15
Thus:
m<1 = 3x + 15 = 3(20) + 15
m<1 = 75°
m<2 = 4x - 5 = 4(20) - 5
m<2 = 75°
m<3 = 5y = 5(15)
m<3 = 75°
m<4 + m<3 = 180° (same side interior angles are supplementary)
m<4 + 75° = 180° (substitution)
m<4 = 180° - 75° (subtraction property of equality)
m<4 = 105°
