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Question

In the adjoining figure the value of x is:


  1. 25

  2. 26

  3. 28

  4. 29


Solution

The correct option is D

29


In ΔADC
CAD+ADC+DCA=180    [Angle sum property]
CAD+ADC+64=180
CAD+ADC=(18064)=116
But CD = CA CAD=ADC [ s opposite to equal sides of a Δ are equal]
So, CAD=ADC=1162=58
Now, ADC=ABD+DAB
[Ext. of a Δ = sum of int. opp. s]
But, AD=BDABD=DAB.
So, ADC=2DAB
DAB=12ADC
x=12×58=29
Hence, x=29

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