Question

braden has a new adjustable outdoor basketball hoop. at its lowest setting, the adjustable bracket makes a 45° angle with the pole. the bracket adjusts to 5 different settings, each 15° more than the previous setting.

Explanation:

Step1: Sum of angles in a semicircle

The sum of angles around a point on a straight line (semicircle) is \(180^{\circ}\).

Step2: Set up the equation

We know that \(x + 45^{\circ}+15^{\circ}+15^{\circ}+15^{\circ}+15^{\circ}=180^{\circ}\).
Simplify the sum of the known angles: \(45^{\circ}+(15^{\circ}\times4)=45^{\circ}+60^{\circ}=105^{\circ}\).
So the equation becomes \(x + 105^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(105^{\circ}\) from both sides of the equation: \(x=180^{\circ}-105^{\circ}\).

Answer:

\(x = 75^{\circ}\)