Problema Solution

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 65 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

Answer provided by our tutors

Let

x = the measure of the first angle, x>0

y = the measure of the second angle, y>0

z = the measure of the third angle, z>0

x + y + z = 180

The measure of the first angle is three times the measure of the second angle:

x = 3y

The measure of the third angle is 65 degrees more than the measure of the second angle:

z = 65 + y

We have the following system of equations:

x + y + z = 180

x = 3y

z = 65 + y
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x = 69 degrees

y = 23 degrees

z = 88 degrees

The measures of the angles in the triangle are: 69 degrees, 23 degrees and 88 degrees.