Question

In the given figure, angle CAB - 40° and angle AKB - 105°.
Find angle KCD.

(1) 65°
(2) 35°
(3) 40°
(4) 72°
​

Answer 1

Answer:

Step-by-step explanation:

angle KCD = 180- 40+105  [ BY ANGLE SUM PROPERTY]

= 180-145

=35

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Answer 2

In the given figure AKB is a Δ, and :-

∠ CAB = 40°, ∠AKB = 105°,

now we have to find out ∠ABK=?

In ΔAKB :-

∠ CAB +∠AKB+∠ABK = 180°

40° +°105°  +∠ABK = 180°

∠ABK = 180° - 145° = 35°

Now we will join A & D.

AD will be a chord

∴ ∠ KCD = ∠ABK = 35°        ( both angles are made by the same chord AD)

Hence proved that ∠ KCD = 35°

Ans :- ( 2 ) 35°

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