Question

in a triangle, one - angle is 52°, another is 64°, and the third is 2r°. r = ____

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we have the equation \(52 + 2r+64 = 180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(52 + 64+2r=116 + 2r\). So, the equation becomes \(116 + 2r=180\).

Step3: Solve for \(r\)

Subtract 116 from both sides: \(2r=180 - 116\), which gives \(2r = 64\). Then divide both sides by 2: \(r=\frac{64}{2}\).

Answer:

32