Given lines p and q are parallel, m<2 - (14x - 12), m<6 - (5y + 23), and m<8 - (8x + 27), solve for the values of x and y then solve for the measure of each angle
Answers
Answer:
x = 7.5
y = 14
m<1 = 87°
m<7 = 93°
Step-by-step explanation:
Given:
m<2 = (14x - 12),
m<6 = (5y + 23),
m<8 = (8x + 27)
m<2 + m<8 = 180° (consecutive exterior angles are supplementary)
(14x - 12) + (8x + 27) = 180 (substitution)
Solve for x
14x - 12 + 8x + 27 = 180
Collect like terms
22x + 15 = 180
Subtract 15 from each side
22x = 180 - 15
22x = 165
Divide both sides by 22
x = 7.5
m<2 = m<6 (corresponding angles are congruent)
(14x - 12) = (5y + 23) (substitution)
Plug in the value of x
14(7.5) - 12 = 5y + 23
105 - 12 = 5y + 23
93 = 5y + 23
Subtract 23 from each side
93 - 23 = 5y
70 = 5y
Divide both sides by 5
14 = y
y = 14
✅m<1 = m<8 (alternate exterior angles are congruent)
m<1 = (8x + 27) (substitution)
Plug in the value of x
m<1 = 8(7.5) + 27 = 87°
m<7 = m<2 (alternate exterior angles are congruent)
m<7 = (14x - 12) (substitution)
Plug in the value of x
m<7 = 14(7.5) - 12 = 93°
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