Question

1. the two triangles are congruent. solve for x. then find the missing angles. (3x - 2)° (x + 80)°

Explanation:

Step1: Set up the equation

Since the two triangles are congruent, their corresponding angles are equal. So, \(3x - 2=x + 80\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(3x-x-2=x - x+ 80\), which simplifies to \(2x-2 = 80\).
Add \(2\) to both sides: \(2x-2 + 2=80 + 2\), so \(2x=82\).
Divide both sides by \(2\): \(x=\frac{82}{2}=41\).

Step3: Find the angle measure

Substitute \(x = 41\) into \(3x - 2\) (or \(x + 80\)). Using \(3x-2\): \(3\times41-2=123 - 2=121^{\circ}\).

Answer:

\(x = 41\), and the measure of the congruent angles is \(121^{\circ}\)