​ In the given figure AE is a straight line. If the ratio of angles ∠1, ∠2, ∠3, ∠4 in the given figure is 1:2 :3 : 4, then find the angles. ​

Question

In the given figure \(\overline {AE}\) is a straight line. If the ratio of angles ∠1, ∠2, ∠3, ∠4 in the given figure is 1:2 :3 : 4, then find the angles.

Answer 1

Given \(\overline {AE}\) is a straight line.

Ratio of angles ∠1, ∠2, ∠3, ∠4 is 1 : 2 : 3 : 4 that is 1x: 2x: 3x: 4x 

The sum of the angles at a point on the same side of the line is 180° 

∠1 + ∠2 + ∠3 + ∠4 = 180° 

⇒ 1x + 2x + 3x + 4x = 180° 

⇒ 10x = 180

⇒ 10x/10 = 180/10

∴ x = 18° 

2x = 2 × 18° = 36° 

3x = 3 × 18° = 54° 

4x = 4 × 18° = 72° 

Therefore the angles are 18°, 36°, 54°, 72°.