Question

solve for x.
27)

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, \(14x - 6=(45)+(7x - 2)\).

Step2: Simplify the equation

First, simplify the right - hand side: \(45+(7x - 2)=7x + 43\). The equation becomes \(14x-6 = 7x + 43\).
Subtract \(7x\) from both sides: \(14x-7x-6=7x - 7x+43\), which simplifies to \(7x-6 = 43\).
Add \(6\) to both sides: \(7x-6 + 6=43 + 6\), so \(7x=49\).

Step3: Solve for \(x\)

Divide both sides by \(7\): \(x=\frac{49}{7}\).

Answer:

\(x = 7\)