The angle as of a triangle are as follows: Angle A is the largest angle; its measure is twice the measure of Angle B. The measure of Angle C is 2 less than half the measure of Angle B. What is the measure of the three angles?

1 Answer
Truong-Son N.
Dec 1, 2015

Well, just remember that the total is #180^@# for any triangle, ever. So, what we can construct are some simple relationships:

#color(green)(/_A = /_A)# (1)

#2/_B = /_A#
#-> color(green)(/_B = (/_A)/2)# (2)

#/_C = (/_B)/2 - 2^@#
#-> color(green)(/_C = (/_A)/4 - 2^@)# (3)

So, we can add them up to write and determine #/_A# (and thus the other two):

#/_A + /_B + /_C = 180^@#

#/_A + (/_A)/2 + (/_A)/4 - 2^@ = 180^@#

#/_A + (/_A)/2 + (/_A)/4 = 182^@#

#(4/_A)/4 + (2/_A)/4 + (/_A)/4 = 182^@#

#4/_A + 2/_A + /_A = 728^@#

#7/_A = 728^@#

#color(blue)(/_A = 104^@)#

And of course, just plug things back into (2) and (3) to finish things up.

#color(blue)(/_B = 52^@)#

#color(blue)(/_C = 24^@)#

We can then verify that we've matched the conditions given. #/_A# is indeed twice #/_B#. #/_C# is indeed #2^@# less than half of #/_B#. Finally, you can easily convince yourself that the three angles add up to #180^@#.

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