the measure of the angles of a triangle are in the extended ratio 3 : 5 : 7 what is the measure of the smallest angle?

Here, sum of ratios = 3 + 5 + 7 = 15
Value of 1 unit = 180 / 15 = 12

So, Ratio measures = 3(12), 5(12), 7(12) = 36, 60, 84

In short, Your Answer would be 36 [ smallest side ]

Hope this helps!

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setukumar345 setukumar345 · Answer 2 · 2022-05-25T05:16:46-04:00

The measure of the smallest angle is 36°.

Triangles:

It is a closed figure having three sides.
It has three angles having the sum of 180°.

How to solve the given problem?

As the angles are in the ratio 3:5:7, Let's consider a ΔABC having the angles in the given ratio.
∴∠A=3k°, ∠B=5k° & ∠C=7k°
As sum of angles of triangle is 180°,
∴ ∠A + ∠B + ∠C = 180°
∴ 3k + 7k + 5k = 180°
∴ 15k = 180°
∴ k = 12°
∴∠A = 3k = 3 × 12 =36°
∴∠B = 5k = 5 × 12 =60°
∴∠C = 7k = 7 × 12 =84°

Thus, the measure of the smallest angle is 36°.

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