Vertically opposite angles are either both acute angles or both obtuse angles. State whether the statement is true or false

Solution:

Given, vertically opposite angles are either both acute angles or both obtuse angles.

We have to determine if the given statement is true or false.

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

From the figure,

The vertically opposite angles are ∠1, ∠3, ∠4 and ∠2.

By the theorem,

∠1 = ∠3

∠2 = ∠4

If one angle is acute, then the other angle will also be acute.

Similarly, if one angle is obtuse, then the other angle will also be obtuse.

Therefore, the given statement is true.

✦ Try This: Supplementary angles are either both acute angles or both obtuse angles. State whether the statement is true or false

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

NCERT Exemplar Class 7 Maths Chapter 5 Problem 68

Vertically opposite angles are either both acute angles or both obtuse angles. State whether the statement is true or false

Summary:

The given statement,”Vertically opposite angles are either both acute angles or both obtuse angles” is true

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