Question

in Fig. 5.26, if x + y =w + z, then prove that AOB is a line.​

Answer 1

Step-by-step explanation:

x+y is a straight line

and w+z is also a straight line

so we can say that AOB is a straight line

Answer 2

Given :-

❍ x + y = w + z

To proff :-

❍ AOB is a line

Proff :-

★ As we know that sum of angles around a point is 360° , So

$⟹\: \: \sf\bold{\purple{x + y + w + z = 360 }}$

$⟹(x + y) + (w + z) = 360 \: \: \sf [ \: Grouping \: ]$

As it is given x + y = w + z , so we can write

$⟹(x + y) + (x + y) = 360$

$⟹2(x + y) = 360$

$⟹ \begin{gathered} \rm (x + y) = \cancel \frac{360}{2} \\ \end{gathered}$

$⟹\sf\bold{\purple{(x + y) = 180}}$

∴ Angle BOC + Angle AOC = 180°

Since the sum of two adjacent angles is 180° therefore their non - common arms form a line

Hence AOB is a line