Two angles and share the common arm and are placed next to each other so that

MATHEMATICS · Subjective · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Two angles

\angle QPR

and

\angle RPS

share the common arm

PR

and are placed next to each other so that

\angle QPR + \angle RPS = 150^\circ

. (i) Explain why

\angle QPR

and

\angle RPS

are called adjacent angles. (ii) Using logical reasoning, decide whether the rays

PQ

and

PS

can lie on the same straight line. Give a clear justification for your answer. (iii) State what special name (if any) can be given to the pair

\angle QPR

and

\angle RPS

. Support your statement with reasons.