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Q.

In the given figure, ∠ ABC = 69°, ∠ ACB = 31°. Then which of the following is the value of ∠ BDC?


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a

 80o

b

 100o

c

 75o

d

 95o 

answer is A.

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Detailed Solution

Given, ∠ ABC = 69°, ∠ ACB = 31°.
Question ImageIn ΔABC, from angle sum property,
We get,
∠CAB+∠ ABC+∠ ACB= 180o
Substituting the value of ∠ABC  = 69°, ∠ ACB = 31°
⇒∠CAB+69°+31°= 180o
⇒∠CAB= 180o-100°
⇒∠CAB=80°
In a circle, we know that angles subtended by the same arc at any point in the same segment of the circle are equal.
Thus, we get
⇒∠CAB=∠BDC
Hence, the measure of ∠BDC is 80°.
Therefore, option 1 is correct.
 
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