Question

ABCD is a rectangle if $\angle BPC={124}^o$ Calculate: $\angle BAP$ and $\angle ADP$.

Answer 1

In a rectangle, diagonals are of equal length and bosect each other $\Rightarrow AP=BP$

Now $\angle APB+\angle BPC={180}^o$ (linear)

$\Rightarrow \angle APB={56}^o$ and $\angle ABP=\angle BAP(AP=BP)$

$\Rightarrow$ In $\Delta ABP$, angle sum is ${180}^o\Rightarrow \angle BAP=\frac{180-56}{2}=62$

Now $\angle APD={124}^o\Rightarrow \angle ADP=\frac{180-124}{2}={28}^o$