Use the diagram below to solve. The m∠ 1 = 29x + 12 and the m∠ 5 = 15x - 8. All lines that appear parallel are parallel.

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°

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