Question

Q16 if two consecutive angles of a cyclic quadrilateral ar ‘x’ and ‘180 – 2x’ . find other two angles.

Answer 1

Given :     ∠A = $x$  and  ∠B = $180-2x$

The value of the two consecutive angles of the cyclic quadrilateral is given and we have to find the value of other two angles.

Solution:

Let A, B, C, D are the angles of the cyclic quadrilateral, in which ∠A and ∠B are the consecutive angles of the cyclic quadrilateral whose values are given in the question.

we have to find the value of ∠C and ∠D.

where, ∠C is the opposite angle of the ∠A  and ∠D is the opposite angle of the ∠B.

As we know, in a cyclic quadrilateral the sum of the opposite angles is equal to 180°.

so,  ∠A + ∠C = 180°

        ∠ C = 180° - ∠A

        ∴  ∠C = $180-x$

and  ∠B  + ∠D = 180°

       ∴ ∠D= 180° - ∠B

      ∠ D = $180-(180-2x)$

    ∴ ∠ D  = $2x$

so, the other angles of the cyclic quadrilateral are ( $180-x$ )and  $2x$ .