Question

In the given figure, $AB=AC$ and $\angle BAC={20}^{\circ }$. Find the sum of $\angle ADC$ and $\angle DAC$

• A. ${55}^{\circ }$
• B. ${80}^{\circ }$
• C. ${70}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${80}^{\circ }$

In $△ABC$,
$AB=AC$ (Given)
$\angle ABC=\angle ACB$ (Isosceles triangle property)
Sum of angles $=180$
$\angle ABC+\angle ACB+\angle BAC=180$
$2\angle ACB+20=180$
$\angle ACB={80}^{\circ }$
Now, $\angle ACB+\angle ACD=180$ (Linear pair)
$80+\angle ACD=180$
$\angle ACD={100}^{\circ }$
Now, sum of angles of triangle $ACD=180$
$\angle ACD+\angle ADC+\angle DAC=180$
$\angle ADC+\angle ACD=180-100$
$\angle ADC+\angle ACD={80}^{\circ }$