In triangle abc, if angle a is thirteen less than angle c and angle b is eleven less than four times angle c, find the measure of each angle.

The measure of each angle of the given triangle ABC is;

∠A = 21°

∠B = 125°

∠C = 34°

Let ∠C be x

We are given;

∠A = x - 13

∠B = 4x - 11

Now, we know that the sum of angles in a triangle is 180°. Thus;

∠A + ∠B + ∠C = 180°

Plugging in the relevant values gives;

(x - 13) + (4x - 11) + x = 180°

x - 13 + 4x - 11 + x = 180°

6x - 24 = 180°

6x = 180 + 24

6x = 204

x = 204/6

x = 34°

Thus; ∠C = 34°

Thus;

∠A = 34 - 13

∠A = 21°

∠B = 4(34) - 11

∠B = 136 - 11

∠B = 125°

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