Prove that the sum of four angles of a quadrilateral ABCD is 360degree.
[Hint: Draw diagonal BD by joining the points B and D and use angle sum property of a triangle for two triangles formed.]
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Consider a quad quadrilateral ABCD.
Join QS.
To\quad prove:∠A+∠B+∠C+∠D=360º
Proof:Consider triangle ABD,
we have,∠A+∠ABD+∠ADB=180º⟹(1)[Using Angle sum property of Triangle]
Similarly,triangle BCD,we have,∠DBC+∠C+∠BDC=180º⟹(2)[Using Angle sum property of Triangle]
On adding (1) and (2),we get∠A+∠ABD+∠ADB+∠DBC+∠C+∠BDC=180º+180º
∠A+∠B+∠C+∠D=360º
Answered by
1
Consider a quad quadrilateral ABCD.
Join QS.
To\quad prove:∠A+∠B+∠C+∠D=360º
Proof:Consider triangle ABD,
we have,∠A+∠ABD+∠ADB=180º⟹(1)[Using Angle sum property of Triangle]
Similarly,triangle BCD,we have,∠DBC+∠C+∠BDC=180º⟹(2)[Using Angle sum property of Triangle]
On adding (1) and (2),we get∠A+∠ABD+∠ADB+∠DBC+∠C+∠BDC=180º+180º
∠A+∠B+∠C+∠D=360º
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