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Question
Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, then ∠AOC =
Options
70°
80°
90°
180°
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Solution
Let us draw the following diagram showing two lines AB and CD intersecting at a point O.
Thus, ∠AOC, ∠COB, ∠AODand ∠BODform a complete angle, that is the sum of these four angle is 360°.
That is,
∠AOC + ∠COB +∠BOD+ ∠AOD = 360° (I)
It is given that
∠AOC + ∠COB + ∠BOD = 270° (II)
Subtracting (II) from (I), we get:
∠AOD = 360° - 270°
∠AOD = 90°
If one of the four angles formed by two intersecting lines is a right angle, then each of the four angles will be a right angle.
So, ∠AOC = \[90^\circ\]
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