In a kite ABCD, longer diagonal BD is drawn. If ∠ABD = 54°and ∠ADB = 50°, then what is the measure (in degrees) of the ∠DCB?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 76.
∠ABD = 54°and ∠ADB = 50°
The sum of the three angles of a triangle is 180°.
So, ∠BAD = 180° - (∠ABD + ∠ADB) = 180° - (54° + 50°) = 180° - 104° = 76°
In a kite, the angles between the unequal sides are equal.
In kite ABCD, sides AB and AD are unequal, and sides CB and CD are unequal. The angles formed by these unequal pairs are ∠BAD and ∠DCB.
Thus, ∠DCB = ∠BAD = 76°