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Tell whether the following statement is true or false:

If one of the four angles formed by two intersecting lines is a right angle, then each of the four angles is a right angle.

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True

False

answer is A.

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Detailed Solution

Given one of the four angles formed by two intersecting lines is a right angle.
Question Image

∠ A O C = 90 °

--- (i)
The measure of

∠ B O D

∠ A O C

and

∠ B O D

are vertically opposite angles.

∠ A O C = ∠ B O D ⇒ 90 °

Therefore,

∠ B O D = 90 °

-----(ii)
The measure of

∠ B O C

is,
Since linear pair is supplementary, therefore,

∠ A O B = 180 °

⇒ ∠ A O C + ∠ B O C = 180 °

⇒ ∠ B O C = 180 ° − ∠ A O C

⇒ ∠ B O C = 180 ° − 90 °

From equation (i),

∠ B O C = 90 °

----- (iii)
The measure of

∠ A O D

is,
As we know that,

∠ B O C

and

∠ A O D

are vertically opposite angles.

∠ B O C = ∠ A O D ⇒ 90 °

Therefore,

∠ A O D = 90 °

------(iv)
Hence,

∠ A O C = 90 °, ∠ B O D = 90 °, ∠ B O C = 90 °

and

∠ A O D = 90 °

.
Therefore, all the four angles are

90 °

.
Given statement is true.
Hence, option 1 is correct.

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