The sum of all __________ of a quadrilateral is 360°. Fill in the blanks to make the statement true.
Solution:
Given, The sum of all __________ of a quadrilateral is 360°
We have to fill in the blanks to make the statement true.
A quadrilateral is a closed shape that is formed by joining four points among which any three points are non-collinear.
Consider a quadrilateral ABCD,
∠1 + ∠2 = ∠A ---------- (1)
∠3 + ∠4 = ∠C ---------- (2)
By angle sum property, the sum of the angles of a triangle is 180°.
In ∆ABC,
∠2 + ∠4 + ∠B = 180° ---------------------- (3)
In ∆ACD,
∠1 + ∠3 + ∠D = 180° ---------------------- (4)
Adding (3) and (4),
∠2 + ∠4 + ∠B + ∠1 + ∠3 + ∠D = 180° + 180°
⇒ (∠1 + ∠2) + ∠B + (∠3 + ∠4) + ∠D = 360°
From (1) and (2),
⇒ ∠A + ∠B + ∠C + ∠D = 360°
Therefore, the sum of all angles of a quadrilateral is 360°.
✦ Try This: The sum of all __________ of a triangle is 180°. Fill in the blanks to make the statement true.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 57
The sum of all __________ of a quadrilateral is 360°. Fill in the blanks to make the statement true.
Summary:
The sum of all the angles of a quadrilateral is 360°.
☛ Related Questions:
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