Question

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

The first triangle is 75 degrees, 60 degrees, and 135 degress.
The second triangle is 70 degrees, 30 degrees, and 100 degress.
The third triangle 60 degrees, 45 degrees, and 105 degrees.
The fourth triangle 30 degrees, 80 degrees, and x


Based on these triangles, which statement about x is true?
Responses
A x = 70, because 180 – (30 + 80) = 70 and 180 – 110 = 70x = 70, because 180 – (30 + 80) = 70 and 180 – 110 = 70
B x = 110, because 180 – (30 + 80) = 70 and 180 – 70 = 110x = 110, because 180 – (30 + 80) = 70 and 180 – 70 = 110
C x = 100, because 180 – (30 + 80) = 80 and 180 – 80 = 100x = 100, because 180 – (30 + 80) = 80 and 180 – 80 = 100
D x = 105, because 180 – (30 + 80) = 70 and 180 – 70 = 105

Answer 1

To find \( x \) in the fourth triangle, we start by recognizing that the sum of the angles in a triangle is always 180 degrees.

In the fourth triangle, we have two angles given: 30 degrees and 80 degrees. We can set up the equation as follows:

\[
x + 30 + 80 = 180
\]

Now, we can simplify this:

\[
x + 110 = 180
\]

Next, subtract 110 from both sides:

\[
x = 180 - 110 = 70
\]

So, \( x = 70 \).

Now, let's check the options provided:

A) \( x = 70 \), because \( 180 - (30 + 80) = 70 \) and \( 180 - 110 = 70 \)

This statement is true.

B) \( x = 110 \), because \( 180 - (30 + 80) = 70 \) and \( 180 - 70 = 110 \)

This statement is false.

C) \( x = 100 \), because \( 180 - (30 + 80) = 80 \) and \( 180 - 80 = 100 \)

This statement is false.

D) \( x = 105 \), because \( 180 - (30 + 80) = 70 \) and \( 180 - 70 = 105 \)

This statement is false.

The correct statement is:

**A) \( x = 70 \), because \( 180 - (30 + 80) = 70 \) and \( 180 - 110 = 70 \)**.