MCQ
In $\triangle\text{PQR},$ if $PQ = QR$ and $\angle\text{Q} = 100^\circ $, then $\angle\text{R}$ is equal to:
- ✓$40^\circ$
- B$80^\circ$
- C$120^\circ$
- D$50^\circ$
✓
Answer
Correct option: A.
$40^\circ$
$\text{In} \ \triangle\text{PQR},$ $\text{PQ} = \text{QR}$
$\text{Let} \ \angle\text{P}=\angle\text{R}=\text{x}$
As we know,
$\therefore\ \angle\text{P}+\angle\text{Q}+\angle\text{R}=\text{180}^{\circ}$ [angle sum property of a triangle]
$\Rightarrow \ \text{x}+100^{\circ}+\text{x}=180^{\circ}$ $[\because\angle\text{Q}=100^{\circ},\text{given}]$
$\Rightarrow \ \text{2x}+100^{\circ}=180^{\circ}$
$\Rightarrow \ \text{2x}=80^{\circ}$
$\Rightarrow \ \text{x}=40^{\circ}$
Hence, $\angle\text{P}=\angle\text{R}=\text{40}^{\circ}$
$\text{Let} \ \angle\text{P}=\angle\text{R}=\text{x}$
As we know,
$\therefore\ \angle\text{P}+\angle\text{Q}+\angle\text{R}=\text{180}^{\circ}$ [angle sum property of a triangle]
$\Rightarrow \ \text{x}+100^{\circ}+\text{x}=180^{\circ}$ $[\because\angle\text{Q}=100^{\circ},\text{given}]$
$\Rightarrow \ \text{2x}+100^{\circ}=180^{\circ}$
$\Rightarrow \ \text{2x}=80^{\circ}$
$\Rightarrow \ \text{x}=40^{\circ}$
Hence, $\angle\text{P}=\angle\text{R}=\text{40}^{\circ}$
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