Question

In the given figure, BD = AD and DC = AC. Find the value of x.

• A. 32°
• B. 48°
• C. 34°

Answer 1

The correct option is A

32°

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In $\Delta$ ABD,

$\angle$BAD = $\angle$DBA = 37${}^{\circ }$

Let $\angle$BDA = y

y + 37${}^{\circ }$ + 37${}^{\circ }$ = 180${}^{\circ }$

y + 74${}^{\circ }$ = 180${}^{\circ }$

y = 106${}^{\circ }$

In $\Delta$ ADC,

DC = AC (given in question)

$\angle$ADC = $\angle$DAC = (180${}^{\circ }$ - 106${}^{\circ }$) = 74${}^{\circ }$ (Linear pair)

$\angle$DAC = $\angle$ADC (Since, DC = AC)

Now, x + 74${}^{\circ }$ + 74${}^{\circ }$ = 180${}^{\circ }$

x = 32${}^{\circ }$

Hence, the value of x = 32${}^{\circ }$