Question

6-1: similar figures; proving triangles similar

1. the ratio of the measures of the three angles in a triangle is 14:5:11. find the measures of the angles. show all work.

1.

Explanation:

Step1: Set up the equation

Let the angles be \(14x\), \(5x\), and \(11x\). Since the sum of angles in a triangle is \(180^{\circ}\), we have \(14x + 5x+11x=180\).

Step2: Simplify the left - hand side

Combine like terms: \((14 + 5+11)x=30x\). So, \(30x = 180\).

Step3: Solve for \(x\)

Divide both sides by \(30\): \(x=\frac{180}{30}=6\).

Step4: Find the measures of the angles

• First angle: \(14x=14\times6 = 84^{\circ}\)
• Second angle: \(5x=5\times6=30^{\circ}\)
• Third angle: \(11x=11\times6 = 66^{\circ}\)

Answer:

The measures of the angles are \(84^{\circ}\), \(30^{\circ}\), and \(66^{\circ}\).