Question

triangle ( abc ) is translated 5 units to the right and 4 units up to create triangle ( abc ).
what is the measure of ( angle b )?

Explanation:

Step1: Use the property of translation

Translation does not change the shape and size of the figure. So, \(\triangle ABC\cong\triangle A'B'C'\).

Step2: Apply the triangle - angle - sum theorem

In \(\triangle ABC\), we know that the sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle A = 80^{\circ}\), \(\angle C=\angle C' = 26^{\circ}\).
We use the formula \(\angle A+\angle B+\angle C=180^{\circ}\).
Substitute the values of \(\angle A\) and \(\angle C\) into the formula: \(80^{\circ}+\angle B + 26^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle B\)

First, simplify the left - hand side of the equation: \(\angle B+106^{\circ}=180^{\circ}\).
Then, subtract \(106^{\circ}\) from both sides: \(\angle B=180^{\circ}- 106^{\circ}\).

Answer:

\(74^{\circ}\)