In the given figure, sides AB and AD of quad. ABCD are produced to E and F respectively. If $∠ C B E = 100^{\circ} t h e n ∠ C D F = ?$

(a) $100^{\circ}$

(b) $80^{\circ}$

(c) $130^{\circ}$

(d) $90^{\circ}$

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Solution

ANSWER:
( b ) 80°
In a cyclic quadrilateral ABCD, we have:
Interior opposite angle, $∠ A D C$ = exterior $∠ C B E$ = 100°
∴ $∠ C D F$ = (180° - $∠ A D C$ ) = (180° - 100°) = 80° (Linear pair)

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In the given figure, sides AB and AD of quad. ABCD are produced to E and F respectively. If ∠CBE=100∘ then ∠CDF=? (a) 100∘ (b) 80∘ (c) 130∘ (d) 90∘

ANSWER: ( b ) 80° In a cyclic quadrilateral ABCD, we have: Interior opposite angle, ∠ADC= exterior ∠CBE = 100° ∴ ∠CDF = (180° - ∠ADC) = (180° - 100°) = 80° (Linear pair)

In the given figure, sides AB and AD of quad. ABCD are produced to E and F respectively. If $∠ C B E = 100^{\circ} t h e n ∠ C D F = ?$

(a) $100^{\circ}$

(b) $80^{\circ}$

(c) $130^{\circ}$

(d) $90^{\circ}$

ANSWER:
( b ) 80°
In a cyclic quadrilateral ABCD, we have:
Interior opposite angle, $∠ A D C$ = exterior $∠ C B E$ = 100°
∴ $∠ C D F$ = (180° - $∠ A D C$ ) = (180° - 100°) = 80° (Linear pair)