In triangle ABC, ∠A=120°, a=3, and b=2. Find angle ∠C to the nearest degree.
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Answer:
\angle ACB=40^{\circ}, \angle ABC=63^{\circ}
Step-by-step explanation:
Finding x:
We know that , because it's a straight line. So,
.
We know that the sum of the angles of any triangle will be .
So, we have that .
Combining like terms on the left gives .
Subtracting from both sides gives
.
Dividing both sides by gives
.
Finding missing angle measures:
.
.
So, and
and we're done!
Note: . Coincidence? If not, try and prove it!