SOLUTION: Two angles of a triangle have the same measure. This measure is equal to one-fourth the measure of the thrid angle. Find the measure of each angle.

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Question 230870: Two angles of a triangle have the same measure. This measure is equal to one-fourth the measure of the thrid angle. Find the measure of each angle.
Answer by likaaka(51) About Me  (Show Source):
You can put this solution on YOUR website!
You must remember that the sum of the interior angles of a triangle equals 180 degrees.
So, if you have two angles that are the same and measure +1%2F4+ of the third, begin by naming the third angle x
+x+%2B+2%281%2F4%29x+=+180+ simplify
+x+%2B+%282%2F4%29x+=+180+ find least common denominator to combine like terms
+%284%2F4%29x+%2B+%282%2F4%29x+=+180+
+%286%2F4%29x+=+180+ now solve for x by multiplying both sides by +4%2F6+
+%284%2F6%29%286%2F4%29x+=+%284%2F6%29%28180%29+
x = 120 so the third angle measures 120 degrees, now solve for the other 2 angles
+%281%2F4%29%2A120+ = 30
So the other two angles are 30 degrees
CHECK:
The sum of the interior angles is 180
120 + 30 + 30 = 180
180 = 180