Question

In the above figure, BE $\parallel$ OD and $\angle$ACB = 45${}^{\circ }$ and $\angle$BAC = 60${}^{\circ }$. What is the value of $\angle$BOD?

• A. 75 ${}^{\circ }$
• B. 135 ${}^{\circ }$
• C. 145 ${}^{\circ }$
• D. 90 ${}^{\circ }$

Answer 1

The correct option is A 75 ${}^{\circ }$

From Legendre's theorem, we know that
"The sum of angles of any triangle is a constant and is equal to
two right angles".
$\therefore$$\angle$ACB + $\angle$ABC + $\angle$BAC= 180${}^{\circ }$
$\Rightarrow$ 60${}^{\circ }$+ 45${}^{\circ }$ + $\angle$ABC = 180${}^{\circ }$
$\Rightarrow$ $\angle$ABC = 75${}^{\circ }$.

$\because$BE $\parallel$ OD
$\angle$ABC = $\angle$BOD
(Corresponding angles)
$\therefore$ $\angle$BOD = 75 ${}^{\circ }$