Question

ABCD is a cyclic quadrilateral. if angle A is equal to (2x+4)°and angle c is equal to (4x-64)° then find the value of x

Answer 1

Answer:

2x +4= 144°

4x - 64= 216°

Answer 2

Given:

ABCD is a cyclic quadrilateral. If angle a is equal to (2x+4)°and angle c is equal to (4x-64)°.

To find:

The value of x.

Solution:

To answer this question, first of all, we should know that in a cyclic quadrilateral ABCD having angle a, angle b, angle c and angle d, the sum of opposite angles is equal to 180° i.e. they are supplementary.

This means,

angle a + angle c = 180°...i

and

angle b + angle d = 180°

Now,

proceeding to the solution, as given, we have,

A cyclic quadrilateral ABCD, where

angle a = (2x + 4)°

and

angle c = (4x - 64)°

So,

2x + 4 + 4x - 64 = 180° (from i)

On solving the above, we get

6x - 60 = 180°

6x = 240°

x = 40°

Hence, the value of x is 40°.