Question

The given figure shows a square $ABCD$ and an equilateral triangle $ABP$. Calculate the value of reflex $\angle APC$

• A. ${215}^0$
• B. ${125}^0$
• C. ${220}^0$
• D. ${225}^0$

Answer 1

The correct option is D ${225}^0$

Refer Figure

Given:

$ABCD$ is a square

$ABP$ is an equilateral triangle

Solution:

$AB=BP=BC$ ($△ABP$ is equilateral and $AB$ and $BC$ belong to a square, hence all are equal)

$\angle ABC=\angle ABP+\angle PBC=60°+\angle PBC$

$90°-60°=\angle PBC$

$\angle PBC=30°$

In $△BPC$

$BP=BC$

$\angle BPC=\angle BCP=\frac{180-\angle PBC}{2}=\frac{150°}{2}=75°$ ( angles opposite to equal sides of a triangle are equal)

$\angle APC=\angle APB+\angle BPC=(60+75)°=135°$

Hence, $\text{Reflex}\angle APC=(360-135)°=225°$