A circle is circumscribed on a quadrilateral ABCD. If ∠DAB = 100°, ∠ADB = 35° and ∠CDB = 40°, then find the measure of ∠DBC.
Answer & explanation
Correct answer: option 2
We know that,
In the case of a cyclic quadrilateral, the sum of opposite angles of the quadrilateral is 180°.
The sum of all internal angles of a triangle is 180°.
We have,
∠DAB = 100°,
∠ADB = 35° and ∠CDB = 40°
Considering ΔDAB,
∠DAB + ∠ADB + ∠DBA = 180°
= 100° + 35° + ∠DBA = 180°
= ∠DBA = 180° - 135° = 45°
= ∠ABD = 45°
Because the circle is circumscribed on a quadrilateral ABCD, ABCD is a cyclic quadrilateral.
So, ∠ADC + ∠ABC = 180°
= (∠ADB + ∠CDB) + (∠ABD + ∠DBC) = 180°
= 35° + 40° + 45° + ∠DBC = 180°
= ∠DBC = 180° - 120°
= ∠DBC = 60°