Question

1. solve for x.

(19x - 18)°
(7x + 1)°
(10x - 9)°

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, \(19x - 18=(7x + 1)+(10x - 9)\).

Step2: Simplify the right - hand side of the equation

First, simplify \((7x + 1)+(10x - 9)\):

$$
LATEXBLOCK0
$$

So the equation becomes \(19x - 18=17x-8\).

Step3: Solve for \(x\)

Subtract \(17x\) from both sides:
\(19x-17x - 18=17x-17x - 8\), which simplifies to \(2x-18=-8\).
Add \(18\) to both sides: \(2x-18 + 18=-8 + 18\), so \(2x = 10\).
Divide both sides by \(2\): \(x=\frac{10}{2}=5\).

Answer:

\(x = 5\)