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2 years ago

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

2 answers:

7 0

8x + 3× + 9x = 180

20x = 180
x = 180/20
x = 9

The smallest angle is: 3×9 = 27 degrees

Note: 180 degrees is the sum of angles in a triangle

Stolb23 [73]2 years ago

6 0

Answer:

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°

9(9) = 81°

The measure of the smallest angle is 27°

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