Question

The sum of the measures of the angles is 180. The sum of the measures of the second and third angles is two times the measure of the first angle. The third angle is 26 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.

Answer 1

(X=60,Y=47,Z=73)

Step-by-step explanation:Start by translating the given information into a system of equations. The sum of the measures of the angles is 180, so we have

x+y+z=180

The sum of the measures of the second and third angles is two times the measure of the first angle, so

y+z−2x+y+z=2=0

The third angle is 26 more than the second, so

z−y+z=y+26=26

Therefore, we have the system of equations

x+y+z=180−2x+y+z=0−y+z=26(1)(2)(3)

Use equations (1) and (2) to find x by eliminating y and z. Multiply equation (2) by −1, and then add to equation (1) to eliminate y and z.

x+y+z2x−y−z3xx=180=0=180=60(4)

Use equations (1) and (3) to eliminate z. Multiply equation (3) by −1, and then add to equation (1) to eliminate z.

x+y+zy−zx+2y=180=−26=154(5)

Substitute x=60 into equation (5) to find

x+2y(60)+2y2yy=154=154=94=47

Now we can substitute x=60 and y=47 into equation (1) to find

x+y+z(60)+(47)+zz+107z=180=180=180=73

The solution is therefore (60,47,73).

Answer 2

60,47,73

Explanation:

Let the first angle be
`a` degrees

Let the second angle be
`b` degrees

Let the third angle be
`c` degrees

It is given that sum of angles is
`180` degrees.

so,
`a+b+c=180` ...(i)

It is given that sum of the measures of the second and third angles is two times the measure of the first angle.

`b+c=2* a` ...(ii)

It is given that the third angle is 26 more than the second.

`c=26+b` ...(iii)

using (ii) and (iii),

`b+b+26=2a`

`b+13=a`

using (i),(ii) and (iii),

`a+b+c=a+a-13+26+b=a+a-13+26+a-13=3a`

`3a=180`

`a=60`

`b=a-13=60-13=47`

`c=26+b=26+47=73`