In a quadrilateral, angles are in the ratio 2:3:4:7. Find all the angles of the quadrilateral. Is ita
convex or a concave quadrilateral?
Answers
Answer:
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°
Step-by-step explanation: