Question

In the given figure, it is known, L1$\parallel$ L2 and $\angle$EBC = 130${}^{\circ }$ and $\angle$ACD = 60${}^{\circ }$. What is the value of $\angle$ACB?

• A. 40${}^{\circ }$
• B. 60${}^{\circ }$
• C. 70${}^{\circ }$
• D. 50${}^{\circ }$

Answer 1

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

$\because$ $\text{L1}$ $\parallel$ $\text{L2}$
$\angle$EBC = $\angle$BCD = 130${}^{\circ }$
(alternate interior angles)
$\therefore$
$\angle$BCD = 130${}^{\circ }$

But $\angle$BCD = ​​​​​​​$\angle$ACB + ​​​​​​​$\angle$ACD
$\Rightarrow$ 130${}^{\circ }$ = ​​​​​​​$\angle$ACB + ​​​​​​​60${}^{\circ }$
$\Rightarrow$ $\angle$ACB = 70${}^{\circ }$