MathematicsABCD is a cyclic quadrilateral in which ∠BCD=100° and ∠ABD=70°. Which of the following is the measure of ∠ADB?

ABCD is a cyclic quadrilateral in which $∠ BCD = 100 °$ and $∠ ABD = 70 °$ . Which of the following is the measure of $∠ ADB$ ?

Given ABCD is a cyclic quadrilateral in which

∠ BCD = 100 °

and

∠ ABD = 70 °

.
Construct a figure according to the given data,

In a cyclic quadrilateral, the opposite angles are supplementary. So,

\Rightarrow ∠ BAD + ∠ BCD = 180 °

\Rightarrow ∠ BAD + 100 ° = 180 °

\Rightarrow ∠ BAD = 80 °

ΔABD

, by angle sum property,

\Rightarrow ∠ ABD + ∠ ADB + ∠ BAD = 180 °

\Rightarrow 70 ° + ∠ ADB + 80 ° = 180 °

\Rightarrow ∠ ADB = 30 °

Hence, the measure of angle

∠ ADB

30 °

.
Therefore, option 1 is correct.

JEE