SOLUTION: please help me solve this The sum of the measures of the angles of any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while the measure of angl

Question 774067: please help me solve this
The sum of the measures of the angles of any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while the measure of angle C is 90 degrees larger than each of A and B. What are the measures of the three angles?
Angle a is
Angle b is
Angle C is

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let the three angles of a triangle be a, b and c.
We are given
(1) a = b
and
(2) c = b + 90
and we know that
(3) a + b + c = 180
Put (1) into (3) and get
(4) b + b + c = 180 or
(5) 2*b + c = 180
Now put (2) into (5) to get
(6) 2*b + b + 90 = 180 or
(7) 3*b = 90 or
(8) b = 30 and from (1) we have
(9) a = 30 and from (2) we have
(10) c = 120
Let's check these values with (3).
Is (30 + 30 + 120 = 180)?
Is (60 + 120 = 180)?
Is (180 = 180)? Yes
Answer: angles a, b and c are 30, 30, and 120 degrees, respectively.
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