In the figure shown, what is the measure of angle x? (5 points)
Triangle ABC has measure of angle BAC equal to 50 degrees, and the measure of angle ABC is equal to 65 degrees. The side BC of the triangle is extended till D. The angle ACD is labeled as x.
115 degrees
130 degrees
145 degrees
150 degrees
To find the measure of angle x, we can use the fact that the sum of the angles in a triangle is 180 degrees.
We are given that the measure of angle BAC is 50 degrees and the measure of angle ABC is 65 degrees.
So, the measure of angle ACB can be found by subtracting the measures of angles BAC and ABC from 180 degrees:
Measure of angle ACB = 180 degrees - 50 degrees - 65 degrees = 180 degrees - 115 degrees = 65 degrees
Since angle x and angle ACB are opposite angles formed by a straight line, they are supplementary. This means that the sum of their measures is 180 degrees.
So, x + 65 degrees = 180 degrees.
Subtracting 65 degrees from both sides of the equation, we get:
x = 180 degrees - 65 degrees = 115 degrees.
Therefore, the measure of angle x is 115 degrees.
So, the correct answer is:
115 degrees