In a triangle, the ratio of two angles is 5:2, and the third angle is equal to the difference between the other two. What is the number of degrees in the smallest angle?

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Answer 1 · 2017-07-15T15:35:05

The smallest angle is #36^o#

Since the ratio of the two angles is 5:2, Let them be #5x# and #2x#

The third angle is the difference between them so 3rd #=5x-2x#

Remember all the angles in a triangle must add to #180^o#
#2x+5x+(5x-2x)=180#

Removing the parentheses we get: #12x-2x=180#
or #10x=180#
#x=18#

So the angles are:

#2x=36#
#5x=90#
#5x-2x=54#

The smallest angle is #36^o#