Question

If A, B, C, D, are the angles of cyclic quadrilateral, then

• A. A + C =
• B. B + D =
• C. A + B =
• D. C + D =

Answer 1

Answer: (A), (B)

The correct options are
A

A + C =

B

B + D =

For a cyclic quadrilateral

Let O be the center of the circle

Then $\angle$BOD = 2$\angle$BAD

Angle made by same arc on the centerof circle is twice the angle made by the same arc on the circumference of circle.

$\angle$BAD = $\frac{1}{2}$$\angle$BOD _________________(1)

Similarly

$\angle$BCD = $\frac{1}{2}$$\angle$DOB _________________(2)

Equation 1 + equation 2

$\angle$BAD + $\angle$BCD = $\frac{1}{2}$($\angle$BOD + $\angle$DOB)

=$\frac{1}{2}$ (${360}^{\circ }$)

= ${180}^{\circ }$

$\angle$A + $\angle$C = ${180}^{\circ }$

Similarly

$\angle$B + $\angle$D = ${180}^{\circ }$

Sum of the opposite angles of cyclic quadrilateral = ${180}^{\circ }$