Question

1. the ratio of the angles in a triangle is 2:3:4. what are the measures of the three angles? 24. three friends, alex, ben, and chris, share a prize in the ratio 4:5:6. if the total prize money is $150, how much does each person receive?

Explanation:

23.

Step1: Calculate the sum of ratio parts

The ratio of angles is \(2:3:4\). The sum of ratio parts is \(2 + 3+4=9\).

Step2: Find the measure of each angle

Since the sum of angles in a triangle is \(180^{\circ}\).

• First - angle: \(\frac{2}{9}\times180^{\circ}=40^{\circ}\)
• Second - angle: \(\frac{3}{9}\times180^{\circ}=60^{\circ}\)
• Third - angle: \(\frac{4}{9}\times180^{\circ}=80^{\circ}\)

Step1: Calculate the sum of ratio parts

The ratio of sharing is \(4:5:6\). The sum of ratio parts is \(4 + 5+6 = 15\).

Step2: Calculate the amount each person gets

• Alex: \(\frac{4}{15}\times150 = 40\) dollars
• Ben: \(\frac{5}{15}\times150=50\) dollars
• Chris: \(\frac{6}{15}\times150 = 60\) dollars

Answer:

The measures of the three angles are \(40^{\circ}\), \(60^{\circ}\), and \(80^{\circ}\).

24.