The 130° angle is supplementary with its adjacent angle (see attachment). Supplementary angles add to equal 180 degrees; you can find the measure of the interior angle by subtracting the measure of the exterior angle from 180.
180 - 130 = 50
Now that you have values for all interior angles, you can set them equal to 180, since the interior angles of all triangles add to equal 180 degrees. Find x.
180 = (3x + 5) + 2x + 50
180 = 3x + 5 + 2x + 50
180 = 5x + 55
125 = 5x
25 = x
To find the largest interior angle, substitute 5 for x and solve.
3x + 5 --> 3(25) + 5 --> 75 + 5 --> 80
2x --> 2(25) --> 50
The third interior angle measure is 50°.
Answer:
80°
