Question

If two lines intersect at a point and if one pair of vertically opposite angles are acute, then the other pair of vertically opposite angles are.

• A. Obtuse
• B. Complementary
• C. Supplementary
• D. Right angle

Answer 1

The correct option is A Obtuse


Given: $\angle$A and $\angle$C are acute angles.
$\angle$A and $\angle$B are linear pair of angles, Hence
$\angle$A+$\angle$B = ${180}^{\circ }$.
$\angle$A is less than ${90}^{\circ }$, therefore $\angle$B must be greater than ${90}^{\circ }$.
Similary, for $\angle$C and $\angle$D, as these two angles also form a linear pair of angles.
$\therefore$ $\angle$D must be greater than ${90}^{\circ }$.
$\therefore$ both the angles are obtuse.