Question

A side of the triangle below has been extended to form an exterior angle of 147°. Find

the value of x

Answer 1

To find the value of x in the triangle, we can utilize the property of exterior angles. By setting up an equation and solving for x, the value is determined to be 106.5 degrees.

Step-by-step explanation:

To find the value of x, we need to apply the property of exterior angles of a triangle. The sum of an exterior angle and its corresponding interior angle is always 180 degrees. So, the measure of the exterior angle is equal to the sum of the other two interior angles.

Let's assume x is one of the interior angles of the triangle. The other two angles would be 180 - x (the first interior angle) and 180 - x (the second interior angle).

Given that one of the exterior angles is 147 degrees, we can set up the equation:

147 = 180 - x + 180 - x

Simplifying the equation, we get:

147 = 360 - 2x

Now, solve for x:

2x = 360 - 147

2x = 213

x = 213/2

x = 106.5 degrees

Answer 2

X+90 = 147 ( sum of two interior angles equals opposite/adjacent exterior angle)

X = 147 - 90

X = 57