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# Lines b and c are parallel. What is the measure of 6?

a) m6 = 45°

b) m6 = 54°

c) m6 = 117°

d) m6 = 126°

Parallel lines never cut (intersect) or meet each other, and they lie on the same plane.

## Answer: The measure of angle 6 for the given diagram is option (b) m6 = 54°.

Let's look into the steps below

**Explanation:**

As you see in the given figure, we have that:

⇒ m∠6 = m∠2 (corresponding angles) ----------- (1)

⇒ m∠6 = (5x + 9)º (vertical angles)

So,

⇒ m∠2 = (5x + 9)º [From (1)] --------------- (2)

Alos, (13x + 9)º + m∠2 = 180º (Linear pair) ------------------ (3)

Substitute (2) in equation (3)

⇒ (13x + 9)º + (5x +9)º = 180º

⇒ (18x + 18)º = 180º

⇒ 18x = 180º - 18º

⇒ x = 9º

Now, we know that

m∠6 = (5x + 9)º

Put the value of x to find m∠6

⇒ m∠6 = (5 × 9 + 9)º

⇒ m∠6 = 54º

### Thus, the measure of the angle 6 is 54º.

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