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.

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

The required value of  three angles first, second, and third angles, respectively x = 118, y = 26 and z = 36.

Given that,

The sum of two measure of the angle of a triangle is 180.

We have to find,

The measures of the three angles. Do not include degree symbol in your answer.

According to the question,

Let, The first angle be = x

the second angle be = y

And the third angle = z

Sum of measures of the angles of a triangle is 180.

Then,

x + y + z = 180

And The sum of the measures of the second and third angles is four times,

x + y = 4z

And The third angle is 10 more than the second,

It can be written as

z = y + 10

Solving the equation 2 and 3

x + y = 4 ( y + 10 )

x + y = 4y + 40

x  = 40 + 3y

Put the value of x in the equation 1

x + y + z = 180

40 + 4y + z = 180

Substitute the value of z from equation 3

40 + 4y + y + 10 = 180

50 + 5y = 180

5y = 180 - 50

5y = 130

y = 26

And

z = 10 + 26 = 36

Again x + 36 + 26 = 180

x = 180 - 62

x = 118

Hence, The required value of  three angles x = 118, y = 26,  z = 36.

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