Question

Four triangles are shown. One side of each triangle lies on a ray, and the triangles are not drawn to scale.


Based in these triangles, which statement about x is true?
Responses
A x = 60, because 180 – (80 + 40) = 60 and 180 – 120 = 60x = 60, because 180 – (80 + 40) = 60 and 180 – 120 = 60
B x = 120, because 180 – (80 + 40) = 60 and 180 – 60 = 120x = 120, because 180 – (80 + 40) = 60 and 180 – 60 = 120
C x = 110, because 180 – (80 + 40) = 60 and 180 – 60 = 110x = 110, because 180 – (80 + 40) = 60 and 180 – 60 = 110
D x = 50, because 180 – (80 + 40) = 50 and 180 – 130 = 50

Answer 1

To determine which statement about \( x \) is true, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Based on the expressions provided in the choices:

1. Calculate the missing angle, assuming one vertex angle is \( x \) and the other two angles in the triangle are 80 degrees and 40 degrees.

Using the equation for the sum of the angles:
\[
x + 80 + 40 = 180
\]

Calculating:
\[
x + 120 = 180
\]
\[
x = 180 - 120
\]
\[
x = 60
\]

Now let's analyze the responses:

- **A** states \( x = 60 \), which is correct considering our calculation.
- **B** states \( x = 120 \), which is not correct since \( x \) should be 60, not 120.
- **C** states \( x = 110 \), which is not correct.
- **D** states \( x = 50 \), which is also not correct.

Thus, the correct statement about \( x \) is:

**A** \( x = 60 \), because \( 180 - (80 + 40) = 60 \).