Answer:
Equation: (29x + 12)° + (15x - 8)° = 180°
x = 4
m∠ 5 = 52°
Step-by-step explanation:
Given:
m∠ 1 = 29x + 12,
m∠ 5 = 15x - 8
Since all lines that appear are parallel, therefore, opposite angles of the quadrilateral are congruent.
Therefore, m<1 = m<4 = 29x + 12
m<4 + m<5 = 180° (linear pair)
(29x + 12) + (15x - 8) = 180° (substitution)
The equation above is what we would use in solving for x. Let's solve for x:
29x + 12 + 15x - 8 = 180
Collect like terms
44x + 4 = 180
Subtract 4 from both sides
44x = 180 - 4
44x = 176
Divide both sides by 44
x = 176/44
x = 4
m∠ 5 = 15x - 8
Plug in the value of x
m∠ 5 = 15(4) - 8 = 60 - 8
m∠ 5 = 52°
