Question

1. find the value of x.

a. 10
b. 7.5
c. 14
d. 12
e. 8

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

So, \((12x - 4)=(10x - 10)+30\)

Step2: Simplify the equation

First, expand the right - hand side: \((12x - 4)=10x - 10 + 30\)

\(12x-4 = 10x+20\)

Then, subtract \(10x\) from both sides: \(12x-10x-4=10x - 10x+20\)

\(2x-4 = 20\)

Next, add \(4\) to both sides: \(2x-4 + 4=20+4\)

\(2x=24\)

Finally, divide both sides by \(2\): \(x=\frac{24}{2}\)

Answer:

\(x = 12\), so the answer is D. 12