Question

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four times the measure of the first angle. The third angle is 10 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles. Do not include degree symbol in your answer.

Answer 1

Answer:x= 36 y= 67 and z=77

Step-by-step explanation: we have to write the equations from the data give in the exercise, this means :

First of all, x,y and z correspònd to the first, second and third angles, respectively.

The sum of the measures of the angles of a triangle is 180

can be written as x+y+z=180

The sum of the measures of the second and third angles is four times the measure of the first angle.  

It can be written by:  x+y=4z

The third angle is 10 more than the second

It can be written as z=y+10

By solving the equations systems the above values can be determined.

x+y+z=180

x+y=4z

z=y+10