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By the Vertical Angles Congruence Theorem (Theorem 2.6), m∠4 = 115°. Lines a and b are parallel, so you can use the theorems about parallel lines.

m∠4 + (x + 5)° = 180° Consecutive Interior Angles Theorem

115° + (x + 5)° = 180° Substitute 115° for m∠4.
x + 120 = 180 Combine like terms.

x = 60 Subtract 120 from each side.7

By the Alternate Exterior Angles Theorem, m∠8 = 120°.
∠5 and ∠8 are vertical angles. Using the Vertical Angles Congruence Theorem
(Theorem 2.6), m∠5 = 120°.
∠5 and ∠4 are alternate interior angles. By the Alternate Interior Angles Theorem,
∠4 = 120°. So, the three angles that each have a measure of 120° are ∠4, ∠5, and ∠8.

By the Linear Pair Postulate (Postulate 2.8), m∠1 = 180° − 136° = 44°. Lines c and d
are parallel, so you can use the theorems about parallel lines.
m∠1 = (7x + 9)° Alternate Exterior Angles Theorem44° = (7x + 9)° Substitute 44° for m∠1.

35 = 7x Subtract 9 from each side.
 5 = x Divide each side by 7.

Draw a diagram. Label a pair of alternate
interior angles as ∠1 and ∠2. You are looking for
an angle that is related to both ∠1 and ∠2. Notice
that one angle is a vertical angle with ∠2 and a
corresponding angle with ∠1. Label it ∠3.