Question

What is the measure of angle ABC given the expressions: (2x + 68) and 7(4x - 2)?

A) 180 degrees
B) 120 degrees
C) 100 degrees
D) 90 degrees

Answer 1

To find the measure of angle ABC, set the expressions equal to each other, solve for x, and substitute the value into one of the expressions.

Step-by-step explanation:

To find the measure of angle ABC, we need to set the two expressions equal to each other and solve for x.

2x + 68 = 7(4x - 2)

First, distribute the 7 on the right side of the equation:

2x + 68 = 28x - 14

Next, combine like terms:

-26x + 68 = -14

Then, subtract 68 from both sides:

-26x = -82

Finally, divide both sides by -26:

x = 3

Now that we have the value of x, substitute it into one of the expressions to find the measure of angle ABC:

2(3) + 68 = 74

Therefore, the measure of angle ABC is 74 degrees.