Question

If the angles of a triangle are in the ratio 3:1:5, then the difference between the greatest and the smallest angles is​

Answer 1

Answer:

80°

Step-by-step explanation:

sum of angles in triangle is 180 deg

let the angles be 3x, x and 5x their ration is 3:1:5

3x+x+5x=180

9x=180

x=20

smallest angle is 20

so largest = 5 × 20=100

difference is 100-20= 80

so answer is 80°

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Answer 2

Given that angles of triangle are in ratio 3:1:5. We have to find difference between greatest and smallest angle.

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In this question, we have given that angles are in ratio 3:1:5. So we know that, sum of angles of triangle is equal to 180°. So here, we can suppose x as common of ratio and then we can compare angles by 180°. This results, we found measures of all angles of triangle and then we can find difference easily.

___________________

Let suppose that x is the common of ratio.

Therefore,

Angles of triangle will be 3x,x and 5x.

Now, we know that sum of angles is equal to 180°.

Therefore,

3x + 1x + 5x = 180°

→9x = 180°

→ x = 180°/9

→ x = 20°

Hence, angles of triangle are :

• 3x = 3×20 = 60°
• x = 20°
• 5x = 5×20 = 100°

Now, we have to find difference between greatest angle and smallest angle. So here, we can see that greatest angle is 100° and Smallest angle is 20°.

Therefore, Different = 100° - 20° = 80°

Conclusion:

• Different between greatest and smallest angle of triangle is 80°

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