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Question 28408: in triangle ABC, the measure of angle C is 18 degrees greater than three times the measure of angle A. the measure of angle B is 5 times the measure of angle A. Find the angles measures.
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! in triangle ABC, the measure of angle C is 18 degrees greater than three times the measure of angle A. the measure of angle B is 5 times the measure of angle A. Find the angles measures.
The problem is given wrong. If the angles have to conform to the angles of a triangle they should always add up to 180 degrees and for the given stipulations, the three angles give their sum which races far far beyond 180
The problem re - formed should be as follows:In triangle ABC, the measure of angle C is 19 degrees greater than the measure of angle A. The measure of angle B is 5 times the measure of angle A. Find the angles measures.
We have A + B + C = 180 ----(*)
C is 19 greater than A which means C = A + 19 ----(1)
B is 5 times A which means B = 5A ----(2)
Puting (1) and (2) in (*),
A+B+C = 180 becomes
A +5A + (A+19) = 180
(A+5A+A) +19 = 180 (by additive commutativity and associativity)
7A= 180 - 19
7A = 161
A = 161/7 = (7X23)/7 = 23
A= 23 in (2) gives B = 5A = 5X23 = 115
and A = 23 in (1) gives C = A + 19 = 23 + 19 = 42
Answer: The three angles are: A = 23 degrees, B = 115 deg and C = 42deg
Verification: A+B+C should be 180
A+B+C = 23+115 +42 = 180
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