Question

A triangle is shown. The base side is extended to the right beyond the triangle. The bottom left angle is labeled x minus five degrees. The top angle is labeled x plus five degrees. The exterior angle on the bottom right is labeled one hundred twenty degrees. Find the value of x . Enter the correct answer in the box.

Answer 1

Answer:To find the value of x in the given triangle, we can consider the following steps:

1. Identify the angles:

The bottom left angle is labeled as x minus five degrees, the top angle is labeled as x plus five degrees, and the exterior angle on the bottom right is labeled as one hundred twenty degrees.

2. Understand the properties of angles in a triangle:

In a triangle, the sum of the interior angles is always 180 degrees. The exterior angle on a vertex is equal to the sum of the two interior angles on the opposite vertices.

3. Set up an equation:

We can set up an equation using the information given:

(x - 5) + (x + 5) + 120 = 180

4. Solve the equation:

Simplifying the equation, we have:

2x + 120 = 180

2x = 180 - 120

2x = 60

x = 60 / 2

x = 30

Therefore, the value of x is 30.

Explanation: