Mathematics

Which of the given statements are correct when two straight lines intersect?
(i) Adjacent angles are complementary.
(ii) Adjacent angles are supplementary.
(iii) Opposite angles are equal.
(iv) Opposite angles are supplementary.


ANSWER

(ii) and (iii) only


SOLUTION
For two straight intersecting lines sum of adjacent angles is $$180^{\circ}$$ and vertically opposite angles are equal.
In the attached figure
$$\angle 1+\angle 2=\angle 2+\angle 3=\angle 3+\angle 4=\angle 4+\angle 1=180^{\circ}$$ (Adjacent angles on straight lines)
$$\angle 1=\angle 3$$ and $$\angle 2 =\angle 4$$  (Opposite angles)
So option $$B$$ is correct.
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