Question

in the given figure AOB is a straight line, if <BOC = 112° and <AOC = 4x, then find x?

please give proper answer​

Answer 1

We know :-

A straight angle = 180°

we have :-

• angle COB = 112°

• angle AOC = 4x

and we know

angle AOB = AOC + COB = 180°

→ 4x + 112° = 180°

→ 4x = 180° - 112

→ 4x = 68

→ x = 17°

Answer 2

Question -

In the given figure AOB is a straight line, if Angle BOC = 112° and Angle AOC = 4x, then find x?

Answer -

We know that both the angles are on a straight line , thus forming linear pair .

This problem can be solved using linear pair property . So what we have now is ,

Let's start calculation ,

$\mapsto\:Angle\:BOC\:+\:Angle\:AOC\:=\:180$

$\mapsto\:112^{\circ}\:+\:4x\:=\:180$

$\mapsto\:4x\:=\:180\:-\:112$

$\mapsto\:4x\:=\:68$

$\mapsto\:x\:=\:\dfrac{68}{4}$

$\boxed{\mapsto\:x\:=\:17}$

Now finding the value of angle AOC ,

We have 4x = Angle AOC

Angle AOC = 4 × 17

Angle AOC = 68

Proving the linear pair property with these values ,

According to the linear pair property the angles that lie on the straight line have their sum equal to 180 degree .

$\mapsto\:Angle\:BOC\:+\:Angle\:AOC\:=\:180$

$\mapsto\:112\:+\:68\:=\:180$

$\mapsto\:180\:=\:180$

Hence proved ✔️