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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
MCQ
In the given figure, $AB \| CD$, If $\angle\text{APQ}=70^\circ$ and $\angle\text{PRD}=120^\circ,$ then $\angle\text{QPR}=?$
  • A
    $35^\circ$
  • B
    $40^\circ$
  • C
    $60^\circ$
  • ✓
    $50^\circ$
✓

Answer

Correct option: D.
$50^\circ$
$\angle\text{APQ}=\angle\text{PQR}=70^\circ$ (Alternate interior angles)
$\angle\text{PRQ}+\angle\text{PRD}=180^\circ$ (Linear Pair)
$\angle\text{PRQ}=180^\circ-120^\circ=60^\circ$
In $\triangle\text{PQR}$
$\angle\text{PQR}+\angle\text{PRQ}+\angle\text{QPR}=180^\circ$ (Angle sum property)
$\angle\text{QPR}=180^\circ-70^\circ-60^\circ=50^\circ.$

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