Question

In the given figure, $AB=AC$ and $\angle BAC={40}^{\circ }$. Find the sum of angle ADC and angle DAC.

• A. ${55}^{\circ }$
• B. ${65}^{\circ }$
• C. ${70}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$

In traingle ABC
$AB=AC$, hence, $\angle ABC=\angle BCA$

Given, $\angle BAC=40$

$\angle ABC+\angle BCA+\angle BAC=180$

$\angle ABC=\angle BCA=\frac{180-40}{2}=70$

therefore, $\angle BCA={70}^{\circ }$
Now, $\angle ACD+\angle ACB=180$
$\angle ACD=110$

In $\Delta ACD$,
$\angle ACD+\angle DAC+\angle ADC=180$
$\angle DAC+\angle ADC={70}^0$