Question

Consider the figure below.

If $\angle A={50}^{\circ }$, and $\angle Q={60}^{\circ }$, then find the value of $\angle B$ (in degrees).

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Answer 1

In the given figure:

In $\Delta ABCand\Delta PQR$

AB = PR (Given)

BC = PQ (Given)

AC = QR (Given)

Therefore, $\Delta ABC\cong \Delta PQR$ by SSS condition.

Therefore,

$\angle A=\angle R={50}^{\circ }$;

$\angle B=\angle P$;

$\angle C=\angle Q={60}^{\circ }$.

Using angle sum property in $\Delta$ ABC,
$\angle A+\angle B+\angle C={180}^{\circ }$
$\Rightarrow$ ${50}^{\circ }+\angle B+{60}^{\circ }={180}^{\circ }$
$\Rightarrow$ $\angle B={70}^{\circ }$