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Standard IX

Mathematics

Sum of Opposite Angles of a Cyclic Quadrilateral

In the given ...

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 = 95° and ∠ECF = 20°. Then, ∠BAD = ?
(a) 95°
(b) 85°
(c) 105°
(d) 75°

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Solution

(c) 105°
We have:
∠ABC + ∠ADC = 180°
⇒ ∠ABC + 95° = 180°
⇒∠ABC = (180° - 95°) = 85°
Now, CF || AB and CB is the transversal.
∴ ∠BCF = ∠ABC = 85° (Alternate interior angles)
⇒ ∠BCE = (85° + 20°) = 105°
⇒ ∠DCB = (180° - 105°) = 75°
Now, ∠BAD + ∠BCD = 180°
⇒ ∠BAD + 75° = 180°
⇒ ∠BAD = (180° - 75°) = 105°

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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 = 95° and ∠ECF = 20°. Then, ∠BAD = ? (a) 95° (b) 85° (c) 105° (d) 75°

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 = 95° and ∠ECF = 20°. Then, ∠BAD = ?
(a) 95°
(b) 85°
(c) 105°
(d) 75°