Question

prove that same of measure of angles quadrilateral is 180​

Answer 1

Step-by-step explanation:

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°. Hence proved.

Answer 2

Answer:

Error in question is that sum of measures of quadrilateral is 360 and not 180

Step-by-step explanation:

Construction: Join any one diagonal.

Proof:

Now the diagonal divided the quadrilateral into 2 triangles

We know that sum of all angles of a triangle is 180

So area of quadrilateral becomes 2 x 180 = 360