Question 1113623: The sum of the measures of the angles is 180 degrees. In triangle ABC, angles A and B have the same measure, while the measure of angle C is 60 degrees larger than each of A and B. What are the measures of the three angles
Found 3 solutions by josgarithmetic, ikleyn, amalm06:
Answer by josgarithmetic(39618)   (Show Source):
Answer by ikleyn(52797)  (Show Source):
You can put this solution on YOUR website! .
The sum of the measures of the angles is 180 degrees. In triangle ABC, angles A and B have the same measure,
while the measure of angle C is 60 degrees larger than each of A and B. What are the measures of the three angles
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Let x = measure of angle A in degrees (the same as that of B, according to the condition).
Then the measure of the angle C is (x+60) degrees.
The sum of interior angles of a triangle is 180 degrees, which gives you an equation
x + x + (x + 60) = 180 degrees
3x + 60 = 180
3x = 180-60 = 120 ====> x =  = 40.
Answer. Measure of angles A and B is 40 degrees. Measure of angle C is 40+60 = 100 degrees.
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Solved.
Be aware: the solution by @josgarithmetic giving the answer "Angle A and B each is 30 degrees and angle C is 120 degrees" is W R O N G.
Answer by amalm06(224)  (Show Source):
You can put this solution on YOUR website! It's an isosceles triangle, since two of the angles are the same.
2x+(x+60)=180
3x=120
x=40
So the angles are 40°,40°, and 100° (Answer)
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