Question

Write and solve an equation that represents the value of x.
(x - 7 ) degrees
43 degrees
Supplementary angles

Answer 1

Supplementary angles are two angles whose measures add up to \(180\) degrees. In this case, you have one angle represented by \((x - 7)\) degrees and the other as \(43\) degrees.

To set up the equation, we can write:

\[
(x - 7) + 43 = 180
\]

Now, let's solve for \(x\):

1. Combine like terms:
\[
x - 7 + 43 = 180
\]
\[
x + 36 = 180
\]

2. Subtract \(36\) from both sides:
\[
x = 180 - 36
\]
\[
x = 144
\]

So, the value of \(x\) is \(144\).

To verify, we can check the measures of both angles:
- The first angle is \(x - 7 = 144 - 7 = 137\) degrees.
- The second angle is \(43\) degrees.

Now, checking the sum:
\[
137 + 43 = 180
\]

This confirms that our solution is correct. Hence, \(x = 144\).