Question

A pair of parallel lines is cut by a transversal. Angle a is located in the upper left exterior next to the transversal, and angle b is located in the bottom right exterior corner of the transversal. If m∠a = (6x - 3)° and m∠b = (9x - 24)°, what is the value of x?

1) 1.4
2) 7
3) 7.8
4) 13.8

Answer 1

By using the corresponding angles postulate, we can set up an equation to solve for x and find that x = 7.

Step-by-step explanation:

Given that angle a is located in the upper left exterior next to the transversal and angle b is located in the bottom right exterior corner of the transversal, and we know that the pair of parallel lines are cut by a transversal, we can determine the relationship between the angles. According to the corresponding angles postulate, when a transversal cuts a pair of parallel lines, the corresponding angles are congruent. So, we can set up an equation to solve for x:

(6x - 3)° = (9x - 24)°

Simplifying the equation, we get:

6x - 3 = 9x - 24

Subtracting 6x from both sides:

-3 = 3x - 24

Adding 24 to both sides:

21 = 3x

Dividing both sides by 3:

x = 7

Therefore, the value of x is 7.