The side QR of Delta PQR is produced to S If ang PRS 105 deg and ang Q 1 2 ang P then what is the va...........

Quantitative Aptitude (CPO) Geometry

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:

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- 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.

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