Answer:
m<7 = 139°
Step-by-step explanation:
Given:
m<3 = (3x + 11)°
m<2 = (4x + 1)°
Required:
m<7 = ?
SOLUTION:
Given that l and m are parallel lines, m<3 and m<2 are alternate interior angles.
Alternate interior angles are congruent. Therefore:
m<3 = m<2
[tex] 3x + 11 = 4x + 1 [/tex] (substitution)
Solve for x
[tex] 3x + 11 - 4x = 4x + 1 - 4x [/tex]
[tex] -x + 11 = 1 [/tex]
[tex] -x + 11 - 11 = 1 - 11 [/tex]
[tex] -x = -10 [/tex]
Divide both sides by -1
[tex] x = 10 [/tex]
Find m<2:
m<2 = (4x + 1)
Plug in the value of x
m<2 = 4(10) + 1 = 40 + 1
m<2 = 41°
Find m<7:
m<2 + m<7 = 180° (consecutive interior angles are supplementary)
41° + m<7 = 180° (substitution)
m<7 = 180 - 41 (subtracting 41 from each side)
m<7 = 139°
