Geometry

Quantitative Aptitude (CPO)

Title

45:30

8 of 24 completed

5 of 15 completed

38 of 100 completed

8 of 20 completed

Indian Economy - Understanding the basics of Indian economic system

The side QR of ΔPQR is produced to S. If ∠PRS = 105° and ∠Q = (1/2)∠P, then what is the value of ∠P?

Options:

- Given: ?PRS (exterior angle) is 105°. Exterior angles in triangles equal the sum of the opposite interior angles.

- Interior angles ?P and ?Q sum up to 105° since ?PRS is the exterior angle.

- Given: ?Q = (1/2)?P.

- Let ?P = x. Therefore, ?Q = x/2.

- The equation becomes x + (x/2) = 105.

- Simplifying: 3x/2 = 105, resulting in x = 70.

- Option:1, 45 - Too low for ?P.

- Option:2, 60 - Incorrect; wouldn't solve the equation.

- Option:3, 70 - Correct! Solves both given conditions.

- Option:4, 75 - Exceeds the sum requirement of angles.