Ex 3.3, 12 (Method 1) Find the measure of ∠P and ∠S if (𝑆𝑃) ̅ ∥ (𝑅𝑄) ̅ (If you find m ∠ R, is there more than one method to find m ∠ P ?) Given ∠R = 90°
∠Q = 130°
SP ∥ RQ
Since SP ∥ RQ
and SR is the transversal
So, ∠ R & ∠ S are angles on the
same side of transversal
∠ R + ∠ S = 180°
90° + ∠ S = 180°
∠ S = 180° – 90°
∠ S = 90°
Since SP ∥ RQ
and QP is the transversal
So, ∠ P & ∠ Q are angles on
the same side of transversal
∠ P + ∠ Q = 180°
∠ P + 130° = 180°
∠ P = 180° – 130°
∠ P = 50°
∴ ∠S = 90° and ∠P = 50°
Ex 3.3, 12 (Method 2) Find the measure of ∠P and ∠S if (𝑆𝑃) ̅ ∥ (𝑅𝑄) ̅ (If you find m ∠ R, is there more than one method to find m ∠ P ?)
Given ∠R = 90°
∠Q = 130° and SP ∥ RQ
We know that
Adjacent angles of a trapezium are Supplementary
∠R + ∠S = 180°
90° + ∠S = 180°
∠S = 180° − 90
∠ S = 90°
∠P + ∠Q = 180°
∠ P + 130° = 180°
∠ P = 180° – 130°
∠ P = 50°

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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