Question

In the given figure, RS is the diameter of the circle. NM is parallel to RS and $\angle MRS={29}^o$. Calculate $\angle RNM$

• A. $\angle RNM={119}^o$
• B. $\angle RNM={19}^o$
• C. $\angle RNM={117}^o$
• D. $\angle RNM={49}^o$

Answer 1

The correct option is A

$\angle RNM={119}^o$

Join RN and MS

RS is the diameter

$\angle RMS={90}^o$ (angle in a semi circle)

$\angle RSM+\angle MRS={90}^0$

$\angle RSM={90}^o-{29}^o={61}^o$

But, $\angle RSM+\angle RNM={180}^0$ (Angles in a cyclic quadrilateral)

${61}^o+\angle RNM={180}^0$

$\angle RNM={180}^o-{61}^o={119}^o$