Question

8. The angles of a triangle are in the ratio 1:3:5. Find the measure of each of the angles.​

Answer 1

✯ Given :

The angles of a triangle are in the ratio 1:3:5. Find the measure of each of the angles.

✯ Answer :

Angles are in ratio = 1:3:5

[ Let, the ratios be x ]

1x + 3x + 5x = 180° [ sum of angles = 180° ]

9x = 180°

x = $\sf\frac{9}{180}$ = $\sf\frac{\cancel{9}}{\cancel{180}}$ = 20°

1st angle = 20°

2nd angle = 3 × 20 = 60°

3rd angle = 5 × 20 = 100°

Hence, the angles are = 20°, 60° and 100°

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✯ Verification :

As we know, sum of angles = 180°

So, 20° + 60° + 100° = 180°

Hence, verified !

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Answer 2

Explanation:

Given:

• Angles of a triangle are in the ratio 1 : 3 :5

To Find:

• What is the meaure of each angle?

Solution: Let x be the common in given ratio. Therefore,

➨ 1st angle = x°

➨ 2nd angle = 3x°

➨ 3rd angle = 5x°

As we know that

★ Sum of all angles of ∆ = 180° ★

$\implies{\rm }$ 1st + 2nd + 3rd = 180°

$\implies{\rm }$ x + 3x + 5x = 180

$\implies{\rm }$ 9x = 180

$\implies{\rm }$ x = 180/9

$\implies{\rm }$ x = 20°

So, the measure of

➬ 1st angle = x = 20°

➬ 2nd angle = 3x = 3(20) = 60°

➬ 3rd angle = 5x = 5+(20) = 100°

______________________

★ Verification ★

=> 20° + 60° + 100° = 180°

=> 180° = 180°

$\large\boxed{\texttt{Verified}}$

★ Area of ∆ = 1/2(Base)(Height)

★ Perimeter of ∆ = Sum of all 3 sides