Question

what is the sum of all the given all interior angels of a quardrillateral
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Answer 1

Answer:

Your answer is 360°

Step-by-step explanation:

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Answer 2

Answer:

A quadrilateral has 4 angles. The sum of its interior angles is 360 degrees.

Step-by-step explanation:

$\large\boxed{ \sf \green{MORE \: \: TO \: \: KNOW }}$

The sum of all interior angles of a quadrilateral is 360⁰

$\green {\underline{ \sf \: Let \: \: For \: \: Example}}$

$\sf \: We \: have \: a \: quadrilateral \: ABCD$

$\sf \: ∠A+∠B+∠C+∠D \: = \: 360 \degree$

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

$\sf \: In △ABC$

$\sf∠CAB+∠ABC+∠BCA \: = \: 180 \degree \\  [ \sf \green{Sum \: of \: all \: three \: angle \: of \: a \: triangle \: is  \: 180 \degree}]$

$\sf \: In △ACD$

$\sf∠CAD+∠ADC+∠DCA=180 \degree  \\ [ \sf \green{Sum \: of \: all \: three \: angle \: of \: a \: triangle \: is \:  180 \degree}]....2$

$\orange{ \boxed{\sf \: Adding \: 1 \: and \: 2 \: we \: get}}$

$( \sf∠CAB \: + \: ∠ABC \: + \: ∠BCA) \: +(∠CAD \: +∠ADC \: +∠DCA) \\ \sf = \: 180 \degree \: +180 \degree$

$\sf \: ∠ABC+∠ADC+(CAB+CAD)+(BCA+DCA)=360 \degree$

$\sf∠ABC+∠ADC+∠BAD+∠BCD=360 \degree$

$\sf∴∠A+∠B+∠C+∠D=360 \degree$