Question

The image shows parallel lines cut by a transversal. The expressions represent unknown angle measurements. What is the value of x?
Responses
A 7
B 10
C 13
D 16

The first equation is x + 55 then x + 93

Answer 1

To find the value of \( x \) when the angle measures are given as \( x + 55 \) and \( x + 93 \) across parallel lines cut by a transversal, we can set up an equation based on the properties of angles formed by a transversal.

Since the angles \( x + 55 \) and \( x + 93 \) are either corresponding angles or alternate interior angles formed by the transversal, they are equal. Therefore, we can set the equations equal to each other:

\[
x + 55 = x + 93
\]

Next, we can solve the equation for \( x \):

1. Subtract \( x \) from both sides:
\[
55 = 93
\]
This is incorrect and shows that the angle values cannot be set equal.

Now, let's check if the angles are supplementary. If they are, we can express that as:

\[
(x + 55) + (x + 93) = 180
\]

Now simplify the equation:

1. Combine like terms:
\[
2x + 148 = 180
\]

2. Subtract 148 from both sides:
\[
2x = 32
\]

3. Now divide by 2:
\[
x = 16
\]

Thus, the value of \( x \) is \( \boxed{16} \).