Final Answer:
In the given situation, the measure of angle 6 is 54 degrees, So the correct option is b.
Step-by-step explanation:
To solve for the measure of angle 6, we first need to understand the relationship between consecutive angles when lines b and c are parallel and a is a transversal.
In the case of parallel lines, consecutive angles (also known as consecutive interior angles or same-side interior angles) are supplementary, which means their sum is equal to 180 degrees.
The two consecutive angles in question are (13x + 9) and (5x + 9). Since these angles are supplementary, we can express their relationship as an equation:
(13x + 9) + (5x + 9) = 180
Now, to find the value of x, we combine like terms and solve for x:
13x + 5x + 9 + 9 = 180
18x + 18 = 180
Subtracting 18 from both sides, we get:
18x = 180 - 18
18x = 162
Now, dividing both sides by 18 to solve for x:
x = 162 / 18
x = 9
With the value of x found, we can now determine the measure of angle 6, which is expressed as (5x + 9). Substituting x with 9, we get:
Angle 6 = 5(9) + 9
Angle 6 = 45 + 9
Angle 6 = 54 degrees
Therefore, the measure of angle 6 is 54 degrees. So the correct option is b.
Complete question:
Lines b and c are parallel, a is transversal, here (13x+9) and (5x+9) are consecutive angles and (5x+9) is equal to angle 6.
What is the measure of angle 6?