Question

what is the value of r? 26.4° 76.3°

Explanation:

Step1: Identify the angle relationship

This is a triangle angle problem where an exterior - like angle (the \(76.3^{\circ}\)) is related to the sum of a non - adjacent interior angle (\(26.4^{\circ}\)) and the angle \(r\). By the exterior angle theorem of triangles, the exterior angle is equal to the sum of the two non - adjacent interior angles. So we can set up the equation \(76.3^{\circ}=26.4^{\circ}+r\).

Step2: Solve for \(r\)

To find \(r\), we subtract \(26.4^{\circ}\) from both sides of the equation.
\(r = 76.3^{\circ}-26.4^{\circ}\)
\(r=49.9^{\circ}\)

Answer:

\(49.9^{\circ}\)