. Construction of a quadrilateral ABCD in which BC= 8 cm, ∠A= 70⁰ ,∠B = 160⁰, ∠C =135⁰ and
AB= 5 cm is not possible because
a) ∠A + ∠B > 180° b)∠A + ∠C> 180°
c) ∠C + ∠B > 180° d) ∠A + ∠B + ∠C >360
Answers
Given : Construction of a quadrilateral ABCD in which BC= 8 cm, ∠A= 70⁰ ,∠B = 160⁰, ∠C =135⁰ and AB= 5 cm is not possible
To Find : Reason
Solution:
∠A= 70⁰ ,∠B = 160⁰, ∠C =135⁰
∠A + ∠B + ∠C = 70⁰ + 160⁰ + 135⁰ = 365⁰
∠A + ∠B + ∠C > 360⁰
Sum of all angles of a quadrilateral is 360⁰
=> ∠A + ∠B + ∠C + ∠D= 360⁰
=> ∠A + ∠B + ∠C = 360⁰ - ∠D
=> ∠A + ∠B + ∠C < 360⁰
Hence Quadrilateral is not possible because
∠A + ∠B + ∠C > 360⁰
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CONSTRUCTION OF A QUADRILATERAL
Given:
A quadrilateral ABCD in which -
- AB = 5cm
- BC = 8cm
- ∠A= 70⁰
- ∠B = 160⁰
- ∠C = 135⁰
To Find:
Reason why the construction of the quadrilateral is not possible.
Solution:
We know that sum of all the interior angles of a quadrilateral is equal to 360°. To understand it in simple words, it is because, if we divide a quadrilateral into two triangles then according to the angle sum property of a triangle, the sum of interior angles of one triangle will be 180°, hence the sum of the interior angles of two triangles will be 360°. Hence, the sum of all the interior angles of a quadrilateral will be 360°.
If we calculate the sum of the above three angles given, then it is as follows:
∠A +∠B + ∠C = 70° + 160° + 135°
= 365°
The sum of the three angles given is already greater than 360° which should not be the case. In order to form a quadrilateral, the sum of given three angles should be less than 360° so that the sum of the fourth angle with the given three angles constitutes to 360°.
Since, ∠A +∠B + ∠C > 360°,
Therefore, the construction of the given quadrilateral is not possible.
Final Answer:
Option (d) ∠A +∠B + ∠C > 360° is the correct answer.
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