Question

1. the ratios of the measures of the angles of a triangle is 5:13:2. find the measures of the angles.

Explanation:

Step1: Set up the equation

Let the angles be \(5x\), \(13x\), and \(2x\). Since the sum of angles in a triangle is \(180^{\circ}\), we have \(5x + 13x+2x=180^{\circ}\).

Step2: Solve for \(x\)

Combine like - terms: \(20x = 180^{\circ}\). Then \(x=\frac{180^{\circ}}{20}=9^{\circ}\).

Step3: Find each angle

For the first angle: \(5x = 5\times9^{\circ}=45^{\circ}\).
For the second angle: \(13x = 13\times9^{\circ}=117^{\circ}\).
For the third angle: \(2x = 2\times9^{\circ}=18^{\circ}\).

Answer:

The measures of the angles are \(45^{\circ}\), \(117^{\circ}\), and \(18^{\circ}\).