Question

In the given figure, if ∠BCA = ∠RPQ = ${15}^o$, then ∠PQR is ___.

• A. ∠PQR = ${35}^o$
• B. ∠PQR = ${15}^o$
• C. ∠PQR = ${45}^o$
• D. ∠PQR =${25}^o$

Answer 1

The correct option is C ∠PQR = ${45}^o$

In $\Delta$ABC and $\Delta$PQR,
Given that:
∠BCA = ∠RPQ = ${15}^o$
BC = PR = 1 Km
AC = PQ = 1.3 Km

Thus, $\Delta$ACB $\cong$ $\Delta$QPR by SAS congruency.
$\Rightarrow$∠PQR = ∠BAC ....(CPCT)

Along the horizontal line through the point A, we have
${90}^o$∠BAC + ${45}^o$ = ${180}^o$
∠BAC = ${180}^o$ - ${45}^o$ - ${90}^o$= ${45}^o$
$\Rightarrow$∠PQR = ∠BAC =${45}^o$.