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Question 403069: the third angle of a triangle is twice the sum of the first two angles; and the first two angles are equal. What is the size (in degrees) for each angle of this triangle?
Answer by rvquartz(19)   (Show Source):
You can put this solution on YOUR website! STEP ONE:
realize that the TOTAL number of degrees in a triangle is 180.
STEP TWO:
Let angle #1 = 'x' degrees
Let angle #2 = 'y' degrees
Let angle #3 = 'z' degrees
STEP THREE:
Now we can model the relationship as:
x + y + z = 180
STEP FOUR:
Realize from the problem statement that
z = 2(x + y)
and also that
x = y
so,
z = 2(x + x) = 4x
STEP FIVE:
since
x + y + z = 180 and since z = 4x we can now write the following
x + y + 4x = 180,
and since x = y, we can now write the following
x + x + 4x = 180, and this is the same as saying that
6x = 180, and now by simple division
x = 180/6 = 30
so x = 30 and since y is the same as x, y is also = 30
and we already established that z = 4x so z = 120
the final answers:
x = 30
y = 30
z = 120
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