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Question
If one of the four angles formed by two intersecting lines is a right angle, then show that
each of the four angles is a right angle.
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Solution
Given,
AB and CD are two lines intersecting at O such that
`∠`BOC = 90°
`∠`AOC = 90°, `∠`AOD = 90° and `∠`BOD = 90°
Proof:
Given that `∠`BOC = 90°
Vertically opposite angles are equal
`∠`BOC = `∠`AOD = 90°
`∠`AOC, `∠`BOC are Linear pair of angles
`∠`AOC + `∠`BOC = 180° [LinearPair]
⇒`∠`AOC + 90° = 180°
⇒ `∠`AOC = 90°
Vertically opposite angles
∴ `∠`AOC = `∠`BOD = 90°
Hence, `∠`AOC = `∠`BOC = `∠`BOD = `∠`AOD = 90°
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