Question

Angle F and angle H are supplementary angles.
* The measure of angle F is 77 degrees
* The measure of angle h is (5x + 18) degrees
Which equation can be used to find the value of x?
A. 77 = 5x + 18
B. 77 + (5x + 18) = 180
C. 77 + (5x + 18) = 90
D. 77 + (5x + 18) = 360
show your work

Answer 1

Supplementary angles are two angles whose measures add up to 180 degrees. We are given:

- Measure of angle F = 77 degrees
- Measure of angle H = (5x + 18) degrees

To find the equation to determine the value of \( x \), we can set up the following equation based on the definition of supplementary angles:

\[
77 + (5x + 18) = 180
\]

This equation states that the sum of the measure of angle F and the measure of angle H is equal to 180 degrees.

Now we can simplify this:

1. Combine like terms:

\[
77 + 5x + 18 = 180
\]

2. Add 77 and 18 together:

\[
95 + 5x = 180
\]

Thus, the equation we want to use to find the value of \( x \) is:

\[
77 + (5x + 18) = 180
\]

So, the correct answer is **B**:

\[
\text{B. } 77 + (5x + 18) = 180
\]