Question

In the figure shown, the two lines are parallel to each other. Which of the following options is incorrect?

• A. $\angle$1 = $\angle$8
• B. $\angle$6 = $\angle$8
• C. $\angle$2 = $\angle$8
• D. $\angle$4 = $\angle$8

Answer 1

The correct option is A

$\angle$1 = $\angle$8

When two lines intersect each other, four angles are formed. The pair of angles which lie on the opposite sides of the point of intersection are called vertically opposite angle. If two parallel lines are cut by a transversal:

(i) Alternate interior angles are equal i.e., $\angle$2 = $\angle$8 and $\angle$3 = $\angle$5.

(ii) Alternate exterior angles are equal i.e., $\angle$1 = $\angle$7 and $\angle$4 = $\angle$6.

(iii) Corresponding angles are equal i.e., $\angle$1 = $\angle$5, $\angle$4 = $\angle$8, $\angle$2 = $\angle$6 and $\angle$3 = $\angle$7.

(iv) Co-interior angles are supplementary i.e., $\angle$2 + $\angle$5 = 180${}^{\circ }$ and $\angle$3 + $\angle$8 =180${}^{\circ }$

$\angle$1 = $\angle$8 is incorrect.