Discussion
S is a point on side PQ of a triangle PQR such that RS = PS = QS. If ∠ QPR = 15°, then the value of (2 ∠ PQR - ∠ PRQ) is :
Answer: B
The value is 60°.
Since PS = QS = RS, S is the midpoint of PQ and is equidistant from P, Q and R, so R lies on the circle with diameter PQ. The angle in a semicircle is a right angle, so ∠PRQ = 90°. (Equivalently, triangles PSR and QSR are isosceles, and their base angles add up to half of 180°.)
\[ \begin{aligned} \angle PQR &= 180^\circ - 90^\circ - 15^\circ = 75^\circ \\ 2\angle PQR - \angle PRQ &= 150^\circ - 90^\circ = 60^\circ \end{aligned} \]
75° is ∠PQR itself, and 50° and 45° do not follow once ∠PRQ is recognised as a right angle.
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