Atriangular playground has angles with measures in ratio 8: 3: 9 what is the measure of the smallest angle

The measure of the smallest angle is 27°

Step-by-step explanation:

The triangle has angles with measure ratio 8:3:9, so the sizes of the angles are going to change depends on the ratio.

Let’s name the common value as “α”.

Basing on the angle-sum property, we already know that the sum of the angle in a triangle is 180°.

The measure of each one are:

8α, 3α, 9α

The sum of these is 180°.

Then,

8α + 3α + 9α = 180°

Let’s sum similar values:

20α =180°

α= 180°/20

α= 9

Replacing values, we going to find the measure of each angle:

8(9) = 72°

3(9) = 27°

9(9) = 81°

The measure of the smallest angle is 27°

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