In a triangle the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 60 degrees more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180 degrees to find the measure of each angle

Question

Matteo

Mathematics

17 October, 09:27

In a triangle the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 60 degrees more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180 degrees to find the measure of each angle

+5

Answers (1)

Know the Answer?

Jovanny Conley · Answer 1

First: 72

Second: 24

Third: 84

Step-by-step explanation:

Let's say that the second angle, the smallest one, is x. Using the provided information, we can make the equation 180=3x+x+x+60, or 180=5x+60. To solve for the second angle, first subtract 60 from each side (120=5x) and then divide each side by five (24=x). Now, to find the first angle, we multiply the second by three (3*24=72). To find the third, add 60 to the second (24+60=84).