Question

In the given figure P, Q and R are collinear points and TQ $\perp$ PR.
(i) Pair of complementary angles.
(ii) Two pairs of supplementary angles.
(iii) Four pairs of adjacent angles.


[3 marks]

Answer 1

(i) Complementary angles are those whose sum is ${90}^{\circ }$.
$\therefore \angle TQS$ and angle SQR are the pair of complementary angles, as their sum is ${90}^{\circ }$.
[1 mark]

(ii) Supplementary angles are those whose sum is ${180}^{\circ }$.
$\therefore \angle SQR,\angle SQP;\angle TQR,\angle TOP$ are pairs of supplementary angles.
[1 mark]

(iii) Two angles are called adjacent angles, if they have a common vertex and a common arm but no common interior points.
$\therefore \angle SQR,\angle SQT;\angle TQR,\angle TQP;\angle SQT,\angle TQP;\angle PQS,\angle SQR$ are pairs of adjacent angles.
[1 mark]