Question

In ray OC stands on line AB such that angle AOC = angle COB,then prove that angle AOC = 90°​

Answer 1

Step-by-step explanation:

Given:-

In ray OC stands on line AB such that angle AOC = angle COB

To find :-

Prove that angle AOC = 90°

Solution :-

Method -1:-

Given that

AB is a line

A ray intersects AB line at O

A ray OC stands on the line AB

Given that

angle AOC = angle COB.

Let angle AOC be X°

Then angle COB = X°

From the figure , angle AOB = 180°

Angles on a straight line add up to 180°.

angle AOB = angle AOC + angle COB.

=> angle AOC + angle COB. = 180°

=> X° + X° = 180°

=> 2X° = 180°

=> X° = 180°/2

=> X° = 90°

=> angle COB = 90°

=> angle AOC = 90°

Both are right angles.

Hence, Proved.

Method -2:-

From the figure ,

angle AOC and angle COB are adjacent angles

and they together gives 180°

They are linear pair.

angle AOB = angle AOC + angle COB.

=> angle AOC + angle COB. = 180°

=> angle AOC + angle AOC = 180°

=> 2×angle AOC = 180°

=> angle AOC = 180°/2

=> angle AOC = 90°

Hence, Proved.

Answer:-

angle AOC is a right angle i.e .angle AOC = 90°

Used formulae:-

• The sum of two adjacent angles is 180° are called Linear pair.
• The angles on a line are Supplementary.
• Angles on a straight line add up to 180°.

Answer 2

$\bold{Concept}$

$\sf{linear \: pair}$ As we know that, linear pair states that angles on a straight line always add up to make 180 degrees.

$\bold{Solution}$

Using linear pair property,

$\tt < COA+<COB=180°$

Let both the angles be X

$\tt \: x + x = 180$

$\tt \: 2x = 180$

$\tt \: x = 90$

Hence prooved.

$\bold \red{Celestial} \bold{Centerix}$