SOLUTION: One of the angle of a triangle is 65. Find the remaining two angles if their difference is 25

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Question 638246: One of the angle of a triangle is 65. Find the remaining two angles if their difference is 25
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the unknown angles +a+ and +b+
The angles of a triangle always add up to 180 degrees, so
(1) +a+%2B+b+%2B+65+=+180+
also given is
(2) +a+-+b+=+25+
---------------
(2) +a+=+b+%2B+25+
Substitute this into (1)
(1) +b+%2B+25+%2B+b+%2B+65+=+180+
(1) +2b+%2B+90+=+180+
(1) +2b+=+90+
(1) +b+=+45+
and, since
(2) +a+=+b+%2B+25+
(2) +a+=+45+%2B+25+
(2) +a+=+70+
The remaining angles are 45 and 70 degrees
check:
(1) +a+%2B+b+%2B+65+=+180+
(1) +70+%2B+45+%2B+65+=+180+
(1) +180+=+180+
OK