A circle is circumscribed on a quadrilateral ABCD. If ∠ DAB = 100°, ∠ ADB = 35° and CDB = 40°, then find the measure of ∠DBC.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 60°
In triangle DAB,
∠DBA + ∠DAB + ∠ADB = 180º
⇒ 100º + 35º + ∠DBA = 180º
⇒ ∠DBA = 45°
Since the circle is circumscribed on a quadrilateral ABCD, ABCD is a cyclic quadrilateral.
So, ∠ADC + ∠ABC = 180°
⇒ (∠ADB + ∠CDB) + (∠ABD + ∠DBC) = 180°
⇒ ∠DBC = 60°
∴ The measure of ∠DBC is 60°.