Question

State true or false

In a square $ABCD$, diagonals meet at $O$. $P$ is a point on $BC$ such that $OB=BP$, then
$\angle BOP=3\angle COP$

• A. True
• B. False

Answer 1

The correct option is A True

Since ABCD is a square.

$AB\parallel CD$ and BD is a transversal.

$\Rightarrow \angle CBD=\angle BDA=45°$ ( alternate interior angles )

$\Rightarrow \angle ADC=90°$

$\Rightarrow \angle BDA+\angle BDC=90°$

$\therefore 45°+\angle BDC=90°$

i.e, $\angle BDC=3\angle POC=67.5°$

$\therefore$ The statement is true.

Hence, the answer is true.