Answer:
[tex]One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o[/tex]
Step-by-step explanation:
Let
x ----> the measure of one angle of the triangle
y ---> the measure of the second angle
z ----> the measure of the third angle
we know that
The sum of the measure of the interior angles in any triangle must be equal to 180 degrees
[tex]x+y+z=180^o[/tex] -----> equation A
One angle of a triangle measures 10 degrees more than the second
[tex]x=y+10[/tex] ----> equation B
The measure of the third angle is twice the sum of the first two angles
[tex]z=2(x+y)[/tex] ---> equation C
substitute equation B in equation C
[tex]z=2(y+10+y)[/tex]
[tex]z=4y+20[/tex] ----> equation D
substitute equation D and equation B in equation A
[tex](y+10)+y+(4y+20)=180^o[/tex]
solve for y
[tex]6y=180-30\\6y=150\\y=25^o[/tex]
Find the value of x
[tex]x=25+10=35^o[/tex]
Find the value of z
[tex]z=4(25)+20=120^o[/tex]
therefore
[tex]One\ angle: 35^o\\Second\ angle: 25^o\\Third\ angle: 120^o[/tex]