# mmathhh

Classified in Mathematics

Written at on English with a size of 51.45 KB.

###### 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° Con****secutive Interior Angles Theorem**

**180° Con**

**secutive Interior Angles Theorem****115° + (x + 5)° = ****180° Substitute 115° for m∠4.**

**x + 120 = 180 ***Combine like terms.*

**180° Substitute 115° for m∠4.**

*Combine like terms.***x = 60 Subtract ****120 from each side.7**

**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.

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.**