In the given figure $, A B = A C$ and $∠ B A C = 30^{o}$ . Find the sum of angle $A D C$ and angle $D A C .$

55^{o}

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65^{o}

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75^{o}

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70^{o}

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Solution

The correct option is C $75^{o}$
As per the given data, $A B = A C$

$∴ ∠ A C B = ∠ A B C = 180 - 30 = 150^{o}$

So, $∠ A C B = ∠ A B C = 75^{o}$

Let, $∠ D A C = x a n d ∠ A D C = y$

Now, $∠ A D C + ∠ D A B + ∠ A B D = 180^{o}$ (property of triangle)

$∴ y + (x + 30) + 75 = 180$

or $x + y = 180 - 105 = 75^{o}$

$∴ ∠ A D C + ∠ D A C = x + y = 75^{o}$

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In the given figure,AB=AC and ∠BAC=30o. Find the sum of angle ADC and angle DAC.

The correct option is C 75o As per the given data,AB=AC∴∠ACB=∠ABC=180−30=150oSo, ∠ACB=∠ABC=75oLet, ∠DAC=xand∠ADC=yNow, ∠ADC+∠DAB+∠ABD=180o (property of triangle)∴y+(x+30)+75=180or x+y=180−105=75o∴∠ADC+∠DAC=x+y=75o

In the given figure $, A B = A C$ and $∠ B A C = 30^{o}$ . Find the sum of angle $A D C$ and angle $D A C .$