Question

1. determine the unknown angle in the triangle pictured below.

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for a triangle with angles \(A = 82^{\circ}\), \(B=45^{\circ}\), and \(C = x^{\circ}\), we have the equation \(A + B + C=180^{\circ}\).

Step2: Substitute the known values into the equation

Substitute \(A = 82\) and \(B = 45\) into \(A + B + C = 180\). We get \(82+45+x = 180\).

Step3: Simplify the left - hand side of the equation

First, calculate \(82 + 45=127\). So the equation becomes \(127+x=180\).

Step4: Solve for \(x\)

Subtract 127 from both sides of the equation. \(x=180 - 127\).

Answer:

\(x = 53\)