Q5 of 32 Page 56

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

Given:


∠x + ∠y = ∠p + ∠q


Theory


A ray possesses 360° when its to original position.


Taking the ray OB


∠x + ∠y + ∠p + ∠q


Forms out a complete circle


Hence;


⇒ ∠x + ∠y + ∠p + ∠q = 360°


If ∠x + ∠y = ∠p + ∠q


Then


(∠x + ∠y) + (∠p + ∠q) = 360°


(∠x + ∠y) + (∠x + ∠y) = 360°


2(∠x + ∠y) = 360°


⇒ (∠x + ∠y) = = 180°


OA and OB are rays joint at O and angle possesses by them ∠ x and ∠ y sums to 180°


Then


⇒ AB is a straight line


More from this chapter

All 32 →
3

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

∠PQS = ∠PRT


 4

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

∠POQ + ∠QOR + ∠SOR + ∠POS = 360°


 1

In figure 5.30 lines AB, CD and EF are parallel.

Find ∠x, ∠y, ∠z and ∠p


 2

In figure 5.31 AB || EF. Find ∠x and ∠y.