Discussion
Angles P and Q of a triangle PQR are respectively 30° and 50°. If the bisectors of angles P and Q meet at a point O, then the value of (2∠POQ − 10°) is :
Answer: C
The value is 270°.
The bisectors split the angles at P and Q in half, so in triangle POQ the angles at P and Q are 15° and 25°.
\[ \begin{aligned} \angle POQ &= 180^\circ - 15^\circ - 25^\circ = 140^\circ \\ 2\angle POQ - 10^\circ &= 280^\circ - 10^\circ = 270^\circ \end{aligned} \]
The same result follows from the rule \(\angle POQ = 90^\circ + \frac{1}{2}\angle R\), with \(\angle R = 100^\circ\). The option 150° comes from using \(\angle P + \angle Q = 80^\circ\) in place of \(\angle POQ\): \(2 \times 80^\circ - 10^\circ = 150^\circ\).
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development