Question

1. solve for x.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. For the triangle in problem (9) with angles 30°, \(4x + 2\), and the third - angle which we don't need to explicitly find, we can set up an equation based on the fact that the exterior angle \(6x + 8\) is equal to the sum of the two non - adjacent interior angles. So, \(6x+8=30+(4x + 2)\).

Step2: Simplify the equation

First, expand the right - hand side: \(6x+8=30 + 4x+2\). Combine like terms: \(6x+8=4x + 32\).

Step3: Solve for \(x\)

Subtract \(4x\) from both sides: \(6x-4x+8=4x-4x + 32\), which gives \(2x+8=32\). Then subtract 8 from both sides: \(2x+8 - 8=32 - 8\), so \(2x=24\). Divide both sides by 2: \(x = 12\).

Answer:

\(x = 12\)