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Q.

In figure, AB = AC, CH = CB and HK ∥ BC, if ∠CAX = 137°,  then what is value of ∠CHK?


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a

30°

b

20°

c

60°

d

43° 

answer is D.

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Detailed Solution

Given, AB = AC, CH = CB and HK ∥ BC.
Question ImageWe know that the sum of two interior angles is equal to the opposite exterior angle in a triangle.
So, ∠DAC = ∠ABC + ∠ACB.
⇒ 137° = 2 ∠ABC
⇒ ∠ABC = 68.5°
∠KHB and ∠HBC are interior angles.
⇒ ∠KHB + ∠HBC = 180°
⇒ ∠KHB + 68.5° = 180°
⇒ ∠KHB = 111.5°
Now, ∠CHB + ∠CHK = ∠BHK
⇒ ∠CHK = 111.5° - 68.5°
⇒ ∠CHK = 43°
Hence, option 4 is correct.
 
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