Question 83353: if you are given an isosolese triangle with the angle 50 given for a , what are all the possible degrees for angle b and c
Found 2 solutions by bucky, Kalmetam:
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You know two key factors:
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1. The sum of the angles in a triangle is 180 degrees
2. In an isosceles triangle, 2 of the angles are equal.
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Let's first suppose that the 50 degrees is the odd angle in that it is NOT one of the pair
of equal angles. Therefore, we can subtract 50 degrees from the 180 degrees in the
triangle and find that the remaining pair of equal angles must total to the missing
130 degrees. So each of the remaining angles must be 1/2 of 130 degrees or 65 degrees.
So, in this case the three angles in the triangle are a = 50 degrees (given), b = 65 degrees,
and c = 65 degrees.
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Another possibility exists. This possibility is that one of the other angles in the triangle
is equal to the given 50 degree angle. Therefore, this triangle has two angles of 50
degrees each for a total of 100 degrees. This time the "odd" angle has to be the remaining
number of degrees in the triangle. The odd angle measure is 180 - 100 = 80 degrees.
So in this triangle the angles are a = 50 degrees (given), b = 50 degrees, and c = 80 degrees
OR a = 50 degrees (given), c = 50 degrees, and b = 80 degrees. (Two cases depending
on the values you select for b and c.)
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Hope this helps you to understand how to find the three possible answers to the problem. Cheers!
Answer by Kalmetam(43) (Show Source):
You can put this solution on YOUR website! Well, a triangle has to add up to 180 degrees in angles, right? So, lets see what we can do!
If to top angle was 50, the two other angles have to be half of the range between 50 and 180 because it's an isoceles triangle and so we get one for each of the following angles.
180-50=130/2=65
A is the top so B and C have to both be 65... If A can be anything, then you can do another technique.
Make it at the bottom and pretend it's one of those two angles... you have to multiply the 50 by 2 and get 100 and then subtract that from 180 so the top angle is 80.
PLEASE READ:
The top one is only if A is strictly the top angle.
Both of them are if A can be any angle.
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