In the figure given below, O is the center of the circle and ∠PQR = 100° and ∠STR = 105°. What is the value (in degrees) of ∠SOP?
Explanation:
Let us join S and R with point X as shown in the figure.
∠SAR = 180° - ∠STR = 180° - 105° = 75°
∠SOR = 2∠SAR = 150°
Now, ∠OSR + ∠ORS + ∠SOR = 180° ⇒ ∠OSR + ∠OSR + 150° = 180° (∠OSR = ∠ORS ) ⇒ ∠OSR = 15° ...(1)
Also, RQRS is a cyclic quadratilateral, hence two opposite angles are supplementary ⇒ ∠PSR + ∠PQR = 180° ⇒ ∠PSR + 100° = 180° ⇒ ∠PSR = 80° ...(2)
From (1) and (2) ∠PSO = 80° - 15° = 65°
In ∆POS ⇒ ∠PSO + ∠SPO + ∠POS = 180° ⇒ 65° + 65° + ∠POS = 180° (∠PSO = ∠SPO) ⇒ ∠POS = 50°
Hence, option (d).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.