Q3 of 32 Page 56

In the given figure 5.16 if ∠ PQR = ∠ PRQ, then prove that

∠PQS = ∠PRT


Given:


∠ PQR = ∠ PRQ


Theory:


A straight line possesses sum of angles to 180°


In Δ PQR


⇒ ∠ PQR = ∠ PRQ


And SQ and RT are stretched side of QR


∴ SQRT is a straight line


As SQRT is a straight line


∠ PQR + ∠ PQS = 180°


∠ PQS = 180° - ∠ PQR


As SQRT is a straight line


∠ PRQ + ∠ PRT = 180°


∠ PRT = 180° - ∠ PRQ


But as ∠ PRQ = ∠ PQR


∠ PRT = 180° - ∠ PQR


∴ ∠ PQS = ∠ PRT


More from this chapter

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1

Angles of degree measure (2x + 4) and (x - 1) are a linear pair of angles. Find them.

 2

From the given figure 5.15


i. Find the measure of ∠BOD.


ii. Find the measure of ∠AOD.


iii. Which are the pairs of vertically opposite angles?


iv. Which are supplementary angles adjacent to ∠AOC? State.

 4

In figure 5.17, OP, OQ, OR and OS are four rays. Prove that

∠POQ + ∠QOR + ∠SOR + ∠POS = 360°


 5

In figure 5.18 if ∠x + ∠y = ∠p + ∠q then prove that AOB is a straight line.