Question

If m∠3 is 124° and m∠4 = 8x + 40, what is the value of x?

Answer 1

To find the value of \( x \), we first need to establish a relationship between the angles given. Suppose \( \angle 3 \) and \( \angle 4 \) are supplementary angles (meaning they add up to \( 180^\circ \)). We can set up the following equation:

\[
m\angle 3 + m\angle 4 = 180^\circ
\]

Substituting the given values:

\[
124^\circ + (8x + 40) = 180^\circ
\]

Now we can simplify and solve for \( x \):

1. Combine like terms:
\[
124 + 8x + 40 = 180
\]
\[
164 + 8x = 180
\]

2. Isolate the term with \( x \):
\[
8x = 180 - 164
\]
\[
8x = 16
\]

3. Divide both sides by 8:
\[
x = \frac{16}{8} = 2
\]

Thus, the value of \( x \) is \( \boxed{2} \).