The measures of the angles of a triangle are in the ratio 4:5:9. What is the measure of the smallest angle of the triangle?

Hello!

Three numbers `a,` `b,` `c` are in the ratio `4:5:9` means that there is a number `x` such that `a = 4x,` `b = 5x,` `c = 9x.`

We know that the sum of angles measures of a triangle is equal to `180` degrees. Thus we obtain the equation for `x,`

`4x + 5x + 9x = 180,` or `(4+5+9)x = 18x = 180,` or `x = 10` (degrees).

So the angles are `4x = 40` degrees, `5x = 50` degrees, `9x = 90` degrees.

The answer: the measure of the smallest angle is 40 degrees.

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