Advertisements
Advertisements
Question
Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, then ∠AOC =
Options
70°
80°
90°
180°
Advertisements
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 = \[90^\circ\]
APPEARS IN
RELATED QUESTIONS
How many pairs of adjacent angles are formed when two lines intersect in a point?
In the below fig, lines PQ and RS intersect each other at point O. If ∠POR: ∠ROQ − 5 : 7,
find all the angles.
In the below fig, lines �1 and �2 intersect at O, forming angles as shown in the figure. If x = 45, Find the values of x, y, z and u.
Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.
In the below fig, rays AB and CD intersect at O.
Determine y when x = 60°
Two straight line AB and CD intersect one another at the point O. If ∠AOC + ∠COB + ∠BOD = 274°, then ∠AOD =
In the given figure, the value of y is
Look at the picture given below. Decide whether the lines given in picture is parallel or perpendicular to each other and write the answer in the box.
Mention two real life situations where we use parallel lines
If the shortest distance between two straight lines in a plane is observed to change, what must be true about the lines?
