Question

In the adjacent figure, Angle POR and Angel QOR form a linear pair.
Ray OS and ray OT are the
bisectors of the respective angles.
(i) If Z ROQ = 70°, find the
measures of Z SOR and Z SOT.
(ii) With help of the figure, show
that, the angle formed by the
bisectors of angles in a linear pair
is a right angle.​

Answer 1

∠POR and ∠QOR form a linear pair,

∴∠POR+∠QOR=180 (Linear pair axiom)

a+b=180 _____ (1)

But a−b=80 _____(2) [Given]

Adding equations (1) and (2), we get

2a=260

∴a= 260/2 =130

Substituting the value of a in (1), we get

130+b=180

⇒b=180−130=50

Answer 2

$\huge \pink {AnSwEr}$

∠POR and ∠QOR form a linear pair,

∴∠POR+∠QOR=180 (Linear pair axiom)

a+b=180 _____ (1)

But a−b=80 _____(2) [Given]

Adding equations (1) and (2), we get

2a=260

∴a= 260/2 =130

Substituting the value of a in (1), we get

130+b=180

⇒b=180−130=50