Question

Please answer the following question​

Answer 1

★ Solution :-

To find the value of the ∠AOD, first we should find the value of the variable x.

To find the value of x, we should use a concept known as the straight line angle property.

Value of x :-

$\sf \leadsto \angle{AOD} + \angle{DOC} + \angle{COB} = {180}^{\circ}$

$\sf \leadsto (2x - 5) + (x - 3) + x = {180}^{\circ}$

$\sf \leadsto (2x + x + x) + ( - 5 - 3) = {180}^{\circ}$

$\sf \leadsto 4x - 8 = {180}^{\circ}$

$\sf \leadsto 4x = 180 + 8$

$\sf \leadsto 4x = 188$

$\sf \leadsto x = \dfrac{188}{4}$

$\sf \leadsto x = 47$

Now, we can find the value of ∠AOD.

Measure of ∠AOD :-

$\sf \leadsto {(2x - 5)}^{\circ} = {2(47)}^{\circ}$

$\sf \leadsto \angle{AOD} = {94}^{\circ}$

Therefore, the value of the ∠AOD is 94°.