Question

the sum of all the interior angles of a quardilateral is what​

Answer 1

Answer:

360 degrees

Step-by-step explanation:

The sum of all interior angles of a quadrilateral is 360  

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We have a quadrilateral ABCD

∠A+∠B+∠C+∠D=360  

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To prove this we join A and C .We draw the diagonal AC

In △ABC

∠CAB+∠ABC+∠BCA=180  

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 [Sum of all three angle of a triangle is 180  

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].....1

In △ACD

∠CAD+∠ADC+∠DCA=180  

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 [Sum of all three angle of a triangle is 180  

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]....2

Adding 1 and 2 we get

(∠CAB+∠ABC+∠BCA)+(∠CAD+∠ADC+∠DCA)=180  

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+180  

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∠ABC+∠ADC+(CAB+CAD)+(BCA+DCA)=360  

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∠ABC+∠ADC+∠BAD+∠BCD=360  

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∴∠A+∠B+∠C+∠D=360  

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