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NTPC Graduate Tier 1 2025 Shift-2 📅 06 Jun, 2025

Let AB and CD be two parallel lines and PQ be a transversal such that PQ intersects AB at the point R and CD at the point S, respectively. If ∠BRP = (2x + 13)° and ∠DSP = (3x - 22)°, then find ∠CSP.

A
105°
B
95°
C
97°
D
83°
Result Summary
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NTPC Graduate Tier 1
2025 • 06 Jun, 2025 • Shift-2
Let AB and CD be two parallel lines and PQ be a transversal such that PQ intersects AB at the point R and CD at the point S, respectively. If ∠BRP = (2x + 13)° and ∠DSP = (3x - 22)°, then find ∠CSP.
Correct Answer
97°
Angle Relationship: When a transversal intersects parallel lines, corresponding angles are equal. Depending on the exact geometric layout, ∠BRP and ∠DSP are......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Geometry
Pg. No -
💡 Analysis & Explanation
Angle Relationship ▼
When a transversal intersects parallel lines, corresponding angles are equal. Depending on the exact geometric layout, ∠BRP and ∠DSP are situated as corresponding angles, meaning we can equate them: (2x + 13) = (3x - 22).
Solving for x ▼
Rearranging the algebraic equation gives 3x - 2x = 22 + 13, which results in x = 35.
Finding the Angles ▼
Substituting x back into the equation for ∠DSP yields 3(35) - 22 = 105 - 22 = 83°.
Linear Pair Concept ▼
Angles on a straight line form a linear pair and add up to 180°. Therefore, ∠CSP + ∠DSP = 180°. Subtracting 83° from 180° gives ∠CSP = 97°.
Conclusion ▼
The accurate measurement of ∠CSP is 97°.
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