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State True/False.

The two lines $AB$ and $CD$ intersect at a point $O$ and $∠ B O C + ∠ A O D = 280 °$ as shown in the figure then the angles $∠ A O D$ and $∠ B O C$ are 140° and $∠ C O A$ and $∠ B O D$ are 40°respectively.

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True

False

answer is A.

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Detailed Solution

Given that the lines AB and CD intersect at a point O and

∠ B O C + ∠ A O D = 280 °

We know that the sum of all the angles making a complete angle is equal to

360 °

.
Thus,

Since

∠ C O A

and

∠ B O D

are vertically opposite angles, thus they are equal to each other.
Hence,
Question Image

Thus,

Since

∠ A O D

and

∠ B O C

are also vertically opposite angles, thus they are equal to each other.
Hence,
Question Image

Thus,

Therefore, the angles

∠ A O D

and

∠ B O C

are 140° and

∠ C O A

and

∠ B O D

are 40° respectively when the two lines

AB

and

CD

intersect at a point

O

and

∠ B O C + ∠ A O D = 280 °

.
Thus, the given statement is true.
Hence, option (1) is correct.

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