Question

In the given figure, if $\angle$ABC = 60 ${}^{\circ }$, $\angle$CAB = 60 and BD is a straight line, ${}^{\circ }$, what is the value of 2 $\angle$ACD?

• A. 100 ${}^{\circ }$
• B. 120 ${}^{\circ }$
• C. 150 ${}^{\circ }$
• D. 240 ${}^{\circ }$

Answer 1

The correct option is D 240 ${}^{\circ }$

From Legendre's theorem, we know,
The sum of angles of a triangle is constant and equal to two right angles
$\Rightarrow$ $\angle$ABC + $\angle$ACB + $\angle$CAB = 180 ${}^{\circ }$
$\Rightarrow$ 60 ${}^{\circ }$ + $\angle$ACB + 60 ${}^{\circ }$ = 180 ${}^{\circ }$
$\Rightarrow$ $\angle$ACB = 60${}^{\circ }$

Now, since BD is a straight line
$\angle$ACB + $\angle$ACD = 180${}^{\circ }$(linear pair)
$\angle$ACD = 120 ${}^{\circ }$
$\therefore$ 2 $\angle$ACD = 2 $\times$ 120 ${}^{\circ }$ = 240 ${}^{\circ }$