In a triangle PQR, if \(\angle P+\angle R=150^\circ\) and \(\angle P+3\angle Q=170^\circ\), then \(\angle P\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 80°
The three angles of a triangle add up to \(180^\circ\). The first condition gives the sum of two angles, so it gives the third angle, \(\angle Q\), at once; the second condition then gives \(\angle P\).
From the angle sum: \(\angle Q=180^\circ-(\angle P+\angle R)=180^\circ-150^\circ=30^\circ\)
Putting \(\angle Q=30^\circ\) in the second condition: \(\angle P+3\times30^\circ=170^\circ\)
So \(\angle P=170^\circ-90^\circ=80^\circ\)