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If one of the angles formed by two intersecting lines is a right angle, what are the other three angles?

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45^{\circ}, 45^{\circ}, 180^{\circ}

90^{\circ}, 90^{\circ}, 90^{\circ}

60^{\circ}, 60^{\circ}, 90^{\circ}

60^{\circ}, 90^{\circ}, 90^{\circ}

answer is B.

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Detailed Solution

It is given a condition that a line is intersected by another line at an angle of

90 °

Let

AB

and

CD

be two lines Intersecting at

O

such that,

∠ AOD = 90^{\circ}

.
Now,

∠ AOD = ∠ COB = 90^{\circ}

… (vertically opposite angles)
⇒

∠ AOD + ∠ DOB = 180^{o}

… (angles on a straight line)
⇒

9 0^{o} + ∠ DOB = 180^{o}

⇒

∠ DOB = 90^{o}

Also,

∠ DOB = ∠ AOC

… (vertically opposite angles)

∠ AOC = 90^{\circ}

Thus, all angles are

90^{o}

.
Hence, the correct option is 2.

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