# In triangle ABC, angle A is 50 degrees greater than angle B, and angle C

October 2, 2021 | education

| **In triangle ABC, angle A is 50 degrees greater than angle B, and angle C is half of the sum of angles A and B. What is the degree measure of angle C?**

By condition, we can make two equations:

<A – <B = 50 ° (1);

<C = (<A + <B) / 2 (2);

We also write that the sum of the angles of the triangle is 180 °:

<A + <B + <C = 180 ° (3);

From (1) we find:

<A = 50 ° + <B (4);

Substitute the expression for angle A into (2)

<C = (50 ° + <B + <B) / 2 = 25 ° + <B (4);

Substitute the expressions for the angles A and C in (3):

50 ° + <B + <B + 25 ° + <B = 180 °;

<B * 3 = 105 °;

<B = 35 °;

Substitute the value of angle B in (1) and (2):

<A = 50 ° + 35 ° = 85 °;

<C = 25 ° + 35 ° = 60 °;

Answer: <A = 85 °, <B = 35 °, <C = 60 °.

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