Question

If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles?
a) \[{45^ \circ },{45^ \circ },{180^ \circ }\]
b) \[{90^ \circ },{90^ \circ },{90^ \circ }\]
c) \[{60^ \circ },{60^ \circ },{90^ \circ }\]
d) \[{60^ \circ },{90^ \circ },{90^ \circ }\]

Answer 1

Hint: Here the question is related to the angles, we have to determine the unknown three angles. The angle of the intersecting lines are known, hence by using the properties of the straight line and angles we determine the unknown values. Then we choose the appropriate option.

Complete step-by-step answer:
The lines are straight lines. These two lines will meet each other. The intersecting lines means the lines which are going to meet at each other.
On considering the given question.
Method one:
The two lines will intersect each other and the one angle formed by the two lines is the right angle and that is \[{90^ \circ }\]. The one of the angles is \[{90^ \circ }\], so the lines will be perpendicular to each other.
On considering the figure

Since it is perpendicular, then the other angles also will be \[{90^ \circ }\].
Therefore the other three angles of the two intersecting lines are \[{90^ \circ }\].
Hence the option b) is the correct one.

Method two:

Let us consider AB and CD as two straight lines. The \[\angle AOC = {90^ \circ }\], COD is a straight line so we have \[\angle AOC + \angle AOD = {180^ \circ }\]. Therefore \[\angle AOD = {90^ \circ }\]. The opposite angles are equal so \[\angle BOD = {90^ \circ }\] and \[\angle BOC = {90^ \circ }\]
Therefore the other three angles of the two intersecting lines are \[{90^ \circ }\].
Hence option B) is the correct one.
So, the correct answer is “Option B”.

Note: Like these kinds of problems we have to consider the diagram, without considering the diagram it will be complicated and the student can’t analyse the problem correctly. We have to know all kinds of angles namely, acute angle, right angle, obtuse angle and straight angle and their measurements.