Question

In a quadrilateral, angles are in the ratio 2:3:4:7. Find all the angles of the quadrilateral. Is it a convex or a concave quadrilateral?
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Answer 1

Step-by-step explanation:

late to is equal to 2x 3x 4x and 7x

then x is equal to

2x+3x+4 x+7x=360 degree

16x=360degree

x is equal to 360/16

x is equal to 22.5 degree

4 x is equal to 22.5×4=90degree

7 x is equal to 22.5×7=157.5degree

3 x is equal to 22.5×3=67.5degree

2x is equal to 22.5×2=45degree

Answer 2

Step-by-step explanation:

Given:

• The angles of a quadrilateral are in ratio 2 : 3 : 4 : 7

To Find:

• What is Measure of each angle of the quadrilateral and which type of quadrilateral is it ?

Solution: Let ABCD be a quadrilateral and x be the common in given ratio such that :-

• ∠A = 2x , ∠B = 3x , ∠C = 4x , ∠D = 7x

As we know that the sum of all the angles of quadrilateral is 360°.

$\implies{\rm }$ ∠A + ∠B + ∠C + ∠D = 360°

$\implies{\rm }$ 2x + 3x + 4x + 7x = 360°

$\implies{\rm }$ 16x = 360°

$\implies{\rm }$ x = 360/16

$\implies{\rm }$ x = 22.5°

So the measure of angles of quadrilateral are:-

➟ ∠A = 2x = 2 $\times$ 22.5 = 45°

➟ ∠B = 3x = 3 $\times$ 22.5 = 67.5°

➟ ∠C = 4x = 4 $\times$ 22.5 = 90°

➟ ∠D = 7x = 7 $\times$ 22.5 = 157.5°

This is a type of convex quadrilateral because measure of all the angles are less than 180°.

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★ Verification ★

➱ ∠A + ∠B + ∠C + ∠D = 360°

➱ 45° + 67.5° + 90° + 157.5° = 360°

➱ 135° + 225° = 360°

➱ 360° = 360°

[ Verified ]