Question

show that the sum of angles of quadrilateral is 180 degree​

Answer 1

Answer:

We have seen in the Triangle Sum Conjecture that the sum of the angles in any triangle is 180 degrees. The Quadrilateral Sum Conjecture tells us the sum of the angles in any convex quadrilateral is 360 degrees. Remember that a polygon is convex if each of its interior angles is less that 180 degree.

Sum of the opposite angles of a cyclic quadrilateral is 180°. But ∠ACB + ∠BAC + ∠ABC = 180° [Sum of the angles of a triangle] ∴ ∠ADC + ∠ABC = 180° ∴ ∠BAD + ∠BCD = 360° – (∠ADC + ∠ABC) = 180°.

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Answer 2

A cyclic quadrilateral's opposite angles add up to 180 degrees. However, ACB + BAC + ABC = 180°

[Sum of Triangle Angles] ADC + ABC = 180° – (ADC + ABC) = 180° BAD + BCD = 360° – (ADC + ABC) = 180°

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