Question

8. The angles of a triangle are in the ratio 1:3:5. Find the measure of each of the angles.
4. One of the acute angles of a right triangle is 50°. Find the other acute angle.
5. One of the angles of a triangle is 110° and the other two angles are equal. What is the
measure of each of these equal angles?
6. If one angle of a triangle is equal to the sum of other two, show that the triangle is a righ
triangle.
Hint. angleA =angleB+angleC = angleA+angleA =angleA+angleB+ angleC = 180°.
7. In a A ABC, if 3 angleA = 4angleB = 6 angleC, calculate the angles.
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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°

✯ Verification :

As we know, sum of angles = 180°

So, 20° + 60° + 100° = 180°

Hence, verified !

Answer 2

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=20

1st angle = 20°

2nd angle = 3 × 20 = 60°

3rd angle = 5 × 20 = 100°

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

As we know, sum of angles = 180°

As we know, sum of angles = 180°So, 20° + 60° + 100° = 180°

HENCE PROVE

calculate the angles is 180