Question

1. use the exterior angle theorem to find the value of $x$.

$x =$

Explanation:

Step1: Apply 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, \(14x - 13=(4x + 13)+(6x + 2)\).

Step2: Simplify the right - hand side

Simplify \((4x + 13)+(6x + 2)\):

$$
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The equation becomes \(14x-13 = 10x+15\).

Step3: Solve for \(x\)

Subtract \(10x\) from both sides: \(14x-10x-13=10x - 10x+15\), which gives \(4x-13 = 15\).
Add \(13\) to both sides: \(4x-13 + 13=15+13\), so \(4x=28\).
Divide both sides by \(4\): \(x=\frac{28}{4}\).

Answer:

\(x = 7\)