Question

Given two parallel lines and a transversal, which pair of angles are equal?

Answer 1

`\sf\\\textsf{The correct answer is (B) }\angle A=\angle E,\ \angle D=\angle H.`

Step-by-step explanation:

`\sf\\\textsf{Here, }\angle A,\ \angle E\ and\ \angle D\ and\ \angle H \textsf{ are the two pairs of corresponding angles, hence}\\\textsf{they are equal.}`

`\sf\\\textsf{Option (A) is not correct because }\angle A\ and\ \angle C \textsf{ are supplementary, since they are}\\\textsf{angles on straight line. }\angle B \textsf{ and }\angle D \textsf{ are also angles on straight line, so their sum}\\\textsf{is also }180^o.`

`\sf\\\textsf{Option (B) is not correct because }\angle C, \angle E \textsf{ and }\angle D,\ \angle F \textsf{ are two pairs of co-interior}\\\textsf{angles, and they are also supplementary to each other.}`

`\sf\\\textsf{Option (D) is also incorrect because the angles claimed to be equal are two pairs}\\\textsf{of angles on a straight line, so }\angle C+\angle D=180^o\ and\ \angle G+\angle H=180^o.`