Two lines intersect such that one of the four angles formed is a right angle. What can you say about the other three angles?

Class 7Lines and AnglesLines and Angles

AAll three are also right angles (90°).
BThey are 90°, 180°, and 90°.
CTwo are acute and one is obtuse.
DThey cannot be determined.

Step-by-Step Solution

If one angle is 90°, its vertical opposite is 90°, and each linear-pair neighbour is 180 − 90 = 90°. So all four are right angles (the lines are perpendicular).

Answer: A) All three are also right angles (90°).

Key idea: Vertically opposite angles

When two straight lines cross, four angles form at the intersection. The two angles directly **across** the vertex (sharing only the vertex, not a side) are called **vertically opposite** — and they are always equal.

If one angle is 70°, then:
- Its vertical opposite is also 70°.
- The other two angles are each 110° (linear pair with 70°).

Why? Each pair forms a linear pair with a common neighbour, both summing to 180° — so the opposites end up equal.

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