Question

The angles of a quadrilateral are in the ratio of 1:2:3:4. What is the measure of the four angles?​

Answer 1

Answer:

sum of 4 angles of a quadrilateral is 360°

so 1st angle is

1/(1+2+3+4)×360°

=1×360°/10

=36°

2nd angle is

2/(1+2+3+4)×360°

=2×36°=72°

3rd angle is

3/(1+2+3+4)×360°

=3×36°

=108°

4th angle is

4/(1+2+3+4)×360°

=4×36°

=144°

Answer 2

✠ Given :-

• The angles in a Quadrilateral are in ratio 1:2:3:4

✠ To find :-

• Measure of each angle

✠ Solution :-

We know that ,

✠ Sum of four angles in a Quadrilateral  is 360°

So, let the angles in a Quadrilateral are

• x
• 2x
• 3x
• 4x

So, these sum should be 360°

⟶x + 2x + 3x + 4x = 360°

⟶10x = 360°

⟶x = 360°/10

⟶x = 36°

✠ Required  angles are :-

⟶x = 36°

2x = 2(36)

⟶2x = 72°  

3x = 3(36)

⟶3x = 108°

4x = 4(36)

⟶4x = 144°

So, the Required angles are 36°, 72°, 108°, 144°

✠ Verification:-

Since , we got 4 angles their sum should be 360°

⟶36° + 72° + 108° + 144°= 360°

⟶360° = 360°

Hence verified !

✠ Know more :-

✠Sum of angles in a Triangle is 180°

✠Sum of angles in a Quadrilateral is 360°

✠Sum of angles in Pentagon is 540°

✠Sum of angles in Hexagon is 720°

✠ Sum of angles in a Septagon is 900°

✠ Sum of angles in a Octogon is 1080°

✠ Sum of angles in a Nonagon is 1260°

✠Sum of angles in any polygon is

(n-2) 180

• n = no.of sides