The angles of a triangle are in the ratio 3:4:5. What is the measure of the smallest angle?

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Answer 1 · 2018-04-30T23:24:11

45 is the smallest angle in your triangle.

The sum of the interior angles of a triangle will be 180#°#.

Therefore, think of the ratios of 3:4:5 as variables followed by "x" (3x, 4x, and 5x).

Combine like terms and set the equation equal to 180, the amt. of degrees in a triangle:

123#x# = 180

Now, divide to isolate for #x#:

#(180/12)# = 15 , so #x# = 15

Now, substitute x for 15 in your variables:

3#x#, 4#x#, and 5#x#
3(15), 4(15), and 5(15)
45, 60, and 75 = 180

Therefore, 45 is the smallest angle.