Question

1. find the value of x:

a. 24
b. 30
c. 6
d. 3

Explanation:

Step1: Use 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, \((4x + 6)=(x + 20)+(2x + 10)\)

Step2: Simplify the equation

Expand the right - hand side: \(4x+6=x + 20+2x + 10\). Combine like terms: \(4x+6 = 3x+30\)

Step3: Solve for \(x\)

Subtract \(3x\) from both sides: \(4x-3x+6=3x - 3x+30\), which gives \(x+6 = 30\). Then subtract \(6\) from both sides: \(x=30 - 6\)

Answer:

A. 24