Question

In the Fig. O is the center of a circle passing through point A, B, C and D and angel ADC= 120° .Find the value of X?

Answer 1

Given:

Angle ADC=120°

To find:

The value of angle x

Solution:

We can find the angle by following the steps given below-

We know that the angle can be found by using the angle sum property of triangles.

AB is the diameter of the circle.

So, angle ACB=90° (Angle in a semi-circle)

Since all the points A, B, C, D lie on the circle, ABCD is a cyclic quadrilateral.

The sum of opposite angles in a cyclic quadrilateral is 180°.

Angle ADC=120° (Given)

Angle ABC+ Angle ADC=180°

Angle ABC=180°-120°

=60°

In ∆ABC, angle ABC+angle ACB+angle BAC=180°

60°+90°+x=180°

150°+x=180°

x=180°-150°

x=30°

Therefore, the value of angle x is 30°.

Answer 2

Answer:

ABCD is a cyclic quadrilateral. we have:

∠ABC+∠ADC=180

∠ABC=180 −120 =60

Also  ∠ACB=90

( angle on a semi circle )

In ΔABC we have

∠BAC+∠ACB+∠ABC=180

∠BAC+90+60 =180

∠BAC=180−150 =30

hope this helps :)