Question

1. the two triangles are congruent. solve for x. then find the missing angles. (2x - 3)° (x + 22)°

Explanation:

Step1: Set up the equation

Since the two triangles are congruent, their corresponding angles are equal. So, \(2x - 3=x + 22\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(2x-x-3=x - x+ 22\), which gives \(x-3 = 22\).
Add \(3\) to both sides: \(x-3 + 3=22+3\), so \(x = 25\).

Step3: Find the measure of the angle

Substitute \(x = 25\) into \(2x - 3\) (or \(x + 22\)). Using \(2x-3\): \(2\times25-3=50 - 3=47^{\circ}\).
Since the sum of angles in a triangle is \(180^{\circ}\) and the two congruent triangles have two equal angles (each \(47^{\circ}\)), the third - angle in each triangle is \(180-(47 + 47)=180 - 94 = 86^{\circ}\).

Answer:

\(x = 25\), the angles are \(47^{\circ},47^{\circ},86^{\circ}\) for each triangle.