Question

basketball sam, kendra, and tony are passing a basketball. if sam is looking at kendra, then he needs to turn 40° to pass to tony. if tony is looking at sam, then he needs to turn 50° to pass to kendra. how many degrees would kendra have to turn her head to look at tony if she is looking at sam?

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). Let the angle at Sam be \(40^\circ\) (since Sam turns \(40^\circ\) to pass to Tony), the angle at Tony be \(50^\circ\) (since Tony turns \(50^\circ\) to pass to Kendra), and the angle at Kendra be \(x\).

Step2: Apply angle sum formula

Using the formula \( \text{Angle at Sam} + \text{Angle at Tony} + \text{Angle at Kendra} = 180^\circ \), substitute the known values: \( 40^\circ + 50^\circ + x = 180^\circ \).

Step3: Solve for \(x\)

First, add \(40^\circ\) and \(50^\circ\): \( 90^\circ + x = 180^\circ \). Then, subtract \(90^\circ\) from both sides: \( x = 180^\circ - 90^\circ = 90^\circ \).

Answer:

\(90^\circ\)