Question

the sum of four angles of a quadritlater is




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Answer 1

Answer:

360°

Interior Angles of a Quadrilateral

The sum of the interior angles of any quadrilateral is 360°. Consider the two examples below. You could draw many quadrilaterals such as these and carefully measure the four angles. You would find that for every quadrilateral, the sum of the interior angles will always be 360°.

Step-by-step explanation:

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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