Question

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basketball sam, kendra, and tony are passing a basketball. if sam is looking at kendra when he needs to turn 40° to pass to tony. if tony is looking at sam when 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?
kendra would have to turn her head ______ degrees to look from sam to tony. i know this because

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). Let the angle at Kendra be \(x\), angle at Sam be \(40^\circ\), angle at Tony be \(50^\circ\). So \(x + 40^\circ+ 50^\circ = 180^\circ\).

Step2: Solve for \(x\)

Simplify the equation: \(x + 90^\circ = 180^\circ\). Subtract \(90^\circ\) from both sides: \(x = 180^\circ - 90^\circ = 90^\circ\)? Wait, no, wait. Wait, the angles here are the turning angles. Wait, actually, when Sam looks at Kendra to Tony, he turns \(40^\circ\), Tony looks at Sam to Kendra, turns \(50^\circ\). So the triangle's angles at Sam, Tony, and Kendra: the angle at Kendra (the turn she needs) is \(180 - 40 - 50 = 90\)? Wait, no, maybe the angles of the triangle. Wait, the sum of angles in a triangle is \(180^\circ\). So if two angles are \(40^\circ\) and \(50^\circ\), the third angle is \(180 - 40 - 50 = 90^\circ\). So Kendra needs to turn \(90^\circ\) because the sum of angles in a triangle is \(180^\circ\), so \(180 - 40 - 50 = 90\).

Answer:

Kendra would have to turn her head \(90\) degrees to look from Sam to Tony. I know this because the sum of the interior angles of a triangle is \(180^\circ\), so \(180^\circ - 40^\circ - 50^\circ = 90^\circ\).