Question 164687
Let's call the angles A,B, and C.
.
.
.
"one angle of a triangle is 20 degrees more than the measure of the second angle"
1.{{{A=B+20}}}
"The measure of the third angle is 30 degrees more than twice the sum of the measures of the first two angles."
2.{{{C=30+2*(A+B)=30+2*(B+20+B)=30+2*(2B+20)}}}
Also, since it's a triangle you know that,
3.{{{A+B+C=180}}}
Use eq. 1 and 2 and substitute in eq.3,

3.{{{A+B+C=180}}}
{{{(B+20)+B+(30+2*(2B+20))=180}}}
{{{B+20+B+30+4B+40=180}}}
{{{6B+90=180}}}
{{{6B=90}}}
{{{highlight(B=15)}}}
from eq.1,
{{{A=B+20}}}
{{{highlight(A=35)}}}
from eq. 2, 
{{{C=30+2*(A+B)}}}
{{{C=30+2*(35+15)}}}
{{{C=30+2*50}}}
{{{highlight(C=130)}}}