Q. 355.0( 1 Vote )
In the given figure, sides AB and AD of quad. ABCD are produced to E and F respectively. If ∠CBE = 100°, then ∠CDF = ?
A. 100o
B. 80o
C. 130o
D. 90o
Answer :
Given: ∠CBE = 100°
Here,
∠ABE = ∠ABC + ∠CBE
180° = ∠ABC + 100°
∠ABC = 180° – 100° = 80°
We know that,
In a cyclic quadrilateral opposite angles are supplementary
∴ ∠ABC + ∠ADC = 180°
80° + ∠ADC = 180°
∠ADC = 180° – 80° = 100°
Here,
∠ADF = ∠ADC + ∠CDF
180° = 100° + ∠CDF
∠CDF = 180° – 100° = 80°
∴ ∠CDF = 80°
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