Question

find value of a with properties used and write them​

Answer 1

Step-by-step explanation:

angle aob = angle eod

foe+eod+doc=180

5a+a+3a=180

9a=180

a=20

Answer 2

Given:

• $\sf{\angle FOE =5a}$
• $\sf{\angle AOB =2a}$
• $\sf{\angle COD=3a}$

To Find:

• The value of unknown variable a .

Concept Used:

• We will make use of concept of Vertically opposite Angle.
• We will make use of measure of angle of a straight line .

Solution:

We have here 3 angles which are

• 3a ,2a and 5a .

(For figure refer to attachment)

So, it is clear from figure that

• AOD is a straight line.
• $\sf{\angle FOE \:and\:\angle BOC}$ are Vertically opposite angle .

We know that , Vertically opposite angles are equal to one another .

So , $\sf{\angle FOE \:=\:\angle BOC=5a}$

Now ,

$\sf{\angle AOB,\:\angle BOC\:\angle COD}$are angles in a straight line .

We know , measure of angle of a straight line is 180°.

Using this ,

$\sf{\implies \angle AOB+\angle BOC+\angle COD =180^{\circ}}$

$\sf{\implies 2a+3a+5a=180^{\circ}}$

$\sf{\implies 10a=180^{\circ}}$

$\sf{\implies a=\cancel{\dfrac{180^{\circ}}{10}}}$

${\underline{\red{\sf{\leadsto x =18^{\circ}}}}}$

Therefore the value of a is 18°.