In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that ∠ADC = 90° and ∠ECF = 20°. Then, ∠BAD = ?

Question

In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that ∠ ADC = 90° and ∠ ECF = 20°. Then, ∠ BAD = ?

Philoid · Accepted Answer

Given: is a cyclic quadrilateral, CF||AB, and

Here, CF|| AB

Hence BC is transversal

∴ ∠ABC = ∠BCF = 85° (Alternate interior angles)

Here,

∠DCB + ∠BCF + ∠ECF = ∠DCE

∠DCB + 85° + 20° = 180°

∠DCB = 180° – 85° – 20° = 75°

We know that,

In a cyclic quadrilateral opposite angles are supplementary

∴ ∠DCB + ∠BAD = 180°

75° + ∠BAD = 180°

∠BAD = 180° – 75° = 105°

∴ ∠BAD = 105°