SOLUTION: One angle of a triangle measures 11°. The other two angles are in a ratio of 3:10. What are the measures of those two angles?

Question 1160835: One angle of a triangle measures 11°. The other two angles are in a ratio of 3:10. What are the measures of those two angles?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

angle A = 11 degrees
angle B = 3x degrees
angle C = 10x degrees

angles B and C are in the ratio 3x:10x which reduces to 3:10 after dividing both parts by x

Angles A,B,C of the triangle add to 180 degrees
A+B+C = 180
11+3x+10x = 180
13x+11 = 180
13x+11-11 = 180-11 ... subtract 11 from both sides
13x = 169
13x/13 = 169/13
x = 13

Using that x value,
angle B = 3x = 3*13 = 39 degrees
angle C = 10x = 10*13 = 130 degrees

Updated angles
angle A = 11 degrees
angle B = 39 degrees
angle C = 130 degrees

Check:
A+B+C = 11+39+130 = 180
the ratio 39:130 reduces to 3:10 after dividing both parts by the GCF 13
That confirms the answers

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