State whether the following statements are true or false?

State true or false: If two lines intersect and if one pair of vertically opposite angles is formed by acute angles, then the other pair of vertically opposite angles will be formed by obtuse angles.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The given statement is true.
Concept: Linear angles concept will be applied. When two lines cross at one point, a linear pair of angles is created. If the angles follow the junction of the two lines in a straight line, they are said to be linear. The sum of the angles in a pair of linear equations is always 180°. These are also referred to as additional angles.
If two lines intersect and if one pair of vertically opposite angles is formed by acute angles, then the other pair of vertically opposite angles will be formed by obtuse angles.
Drawing the figure using the problem given in the question,
It’s clearly visible; angle AOC and angle BOD are obtuse angles, which are vertically opposite to each other.
Hence, the given statement is true.

Watch 3-min video & get full concept clarity