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In the given figure, $A O B$ is a straight line. If $∠ A O C = 4 x °$ and $∠ B O C = 5 x °$ , then from the following choices, find the value of $∠ A O C$ .

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40 °

60 °

80 °

100 °

answer is C.

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Detailed Solution

It is given that

A O B

is a straight line.
We have to find the value of

∠ A O C

.
From the diagram,

∠ A O C = 4 x °

and

∠ B O C = 5 x °

.
The sum of angles on a straight line is equal to

180 °

, hence,

∠ A O C + ∠ B O C = 180 °

.
Substituting and calculating the above equation to get the value of

x

∠ A O C + ∠ B O C = 180 °

4 x + 5 x = 180 °

9 x = 180 °

x = 20 °

Calculate the value of

4 x

to get

∠ A O C

∠ A O C = 4 x

= 4 (20 °) = 80 °

The value of

∠ A O C

80 °

.
Hence option 3) is correct.

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