Question

solve for x.
9)
10)
11)

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.
For problem 9, in \(\triangle PQR\), \(\angle PRH\) is an exterior angle. So, \(\angle PRH=\angle QPR+\angle PQR\).
We know that \(\angle QPR = 30^{\circ}\), \(\angle PQR=(4x + 2)^{\circ}\) and \(\angle PRH=(8 + 6x)^{\circ}\).
Then the equation is \(8+6x=30+(4x + 2)\).

Step2: Simplify the equation

First, simplify the right - hand side of the equation: \(30+(4x + 2)=4x+32\).
The equation becomes \(8 + 6x=4x+32\).
Subtract \(4x\) from both sides: \(8+6x-4x=4x + 32-4x\), which gives \(8 + 2x=32\).
Subtract 8 from both sides: \(2x=32 - 8\), so \(2x=24\).
Divide both sides by 2: \(x=\frac{24}{2}\).

Answer:

\(x = 12\)