Question

test prep consider the diagram.

(x + 5)°

(x - 5)°
120°
find the value of x.
enter the correct answer in the box.
show hints

Explanation:

Step1: Find the adjacent interior angle

The angle adjacent to \(120^\circ\) on the triangle is supplementary to it, so it is \(180 - 120 = 60^\circ\).

Step2: Use triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \((x - 5) + (x + 5) + 60 = 180\).
Simplify: \(x - 5 + x + 5 + 60 = 180\) → \(2x + 60 = 180\).

Step3: Solve for x

Subtract 60: \(2x = 180 - 60 = 120\).
Divide by 2: \(x = \frac{120}{2} = 60\).

Answer:

60