# Answer the following questions? 1) What the angle vertical to ∠NOM 2) What is the angle vertical to ∠TLK 3) Identify the pair of angles supplementary to ∠NOM 4) What the measurement of angles ∠1, ∠2, and ∠3 5) What is the measure of exterior ∠OPS?

Dec 21, 2016

#### Explanation:

(1) The angle vertically opposite to $\angle N O M$ is $\angle L O P$ i.e. $\angle 2$.

(2) The angle vertically opposite to $\angle T L K$ is $\angle O L P$ i.e. $\angle 1$.

(3) The pair of angles supplementary to $\angle N O M$ are $\angle M O P$ and $\angle N O L$.

(4) As $\angle 2$ is vertically opposite to angle $\angle N O M = {97}^{\circ}$, $\angle 2 = {97}^{\circ}$; $\angle 1$ is vertically opposite to angle $\angle T L K = {42}^{\circ}$, $\angle 2 = {42}^{\circ}$. Hence as sum of the angles of a triangeis ${180}^{\circ}$, $\angle 3 = {180}^{\circ} - {97}^{\circ} - {42}^{\circ} = {41}^{\circ}$.

(5) As $\angle 3 = {41}^{\circ}$ and $\angle O P S$ is supplementary to this, $\angle O P S = {180}^{\circ} - {41}^{\circ} = {139}^{\circ}$.