Question

Find the value of x. Then find the measure of each labeled angle.

In a triangle, if (x-26)° represents one of the angles, what is the value of x?
A) x = 32, angle measure = 6°
B) x = 58, angle measure = 32°
C) x = 26, angle measure = 0°
D) x = 0, angle measure = -26°

Answer 1

To find the value of x, we set up an equation involving the sum of the angles in a triangle. Solving for x, we find that x = 26. The measure of each labeled angle can then be found by subtracting x-26 from 180.

Step-by-step explanation:

To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees. So, if (x-26) represents one of the angles in the triangle, then the sum of the other two angles must be equal to 180 - (x-26).

Simplifying this expression, we get 180 - x + 26 = 180 - x + 26 - 26.

Combining like terms, we get 180 - x + 26 = 180.

Therefore, x - x + 26 = 0, and solving for x, we find x = 26.

Now, we can find the measure of each labeled angle. One angle is (x-26) = (26-26) = 0 degrees. The other two angles must add up to 180 - (x-26) = 180 - (26-26) = 180 degrees. Therefore, each angle is 90 degrees.