Question

In the the given figure, angle BCD= 100°, angle ABD= 70°, Find the value of x.
Please teach me step by step.​

Answer 1

Answer :-

In the figure ABCD is a cyclic quadrilateral.

We know that,

Sum of opposite angles of cyclic quadrilateral is 180°.

So, here ∠BCD and ∠BAD are opposite angle of cyclic quadrilateral ABCD.

⇒ ∠BCD + ∠BAD = 180°

⇒ 100 + ∠BAD = 180

⇒ ∠BAD = 180 - 100

⇒ ∠BAD = 80°

Applying angle sum property in triangle ABD -

⇒ ∠BAD + ∠DBA + ∠BDA = 180°

⇒ 80 + 70 + x = 180

⇒ x + 150 = 180

⇒ x = 180 - 150

⇒ x = 30°

Value of x = 30°