Problema Solution
In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 60 degrees greater than that of angle A. Find the measures of the angles.
Answer provided by our tutors
let
a = angle A
b = angle B
c = angle C
the angle C is six times as large as angle A
c = 6a
the measure of angle B is 60 degrees greater than that of angle A
b = 60 + a
since a, b and c are angles of triangle we have
a + b + c = 180
by solving the system of equations
c = 6a
b = 60 + a
a + b + c = 180
we find
a = 15 degrees
b = 75 degrees
c = 90 degrees
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the angles of the triangle ABC are 15 degrees, 75 degrees and 90 degrees.