Question

In the adjoining figure $p\left|\right|q$, $\angle 1=100°$ and $\angle 2=150°$find $\angle x,\angle y,and\angle z.$

Answer 1

Step 1: Find the value of $\angle x$

Given:

$\angle 1=100°$ and $\angle 2=150°$

From diagram$\angle x$ and $\angle 1$ are interior angles on same side of transversal.

$\Rightarrow \angle x+\angle 1=180°$ $[\because$interior angles on same side of transversal are supplementary angles]

$\Rightarrow \angle x+100°=180°$

$$\begin{gathered} \Rightarrow \angle x=180°-100° \\ \Rightarrow \angle x=80° \end{gathered}$$

Step 2: Find the value of $\angle y$

$\angle x$and $\angle y$ are linear pair angles.

$\Rightarrow \angle x+\angle y=180°$ $[\because$linear pair angles are supplementary angles]

$\Rightarrow 80°+\angle y=180°$

$\Rightarrow \angle y=180°-80°$

$\Rightarrow \angle y=100°$

Step 3: Find the value of $\angle z$

$\Rightarrow \angle z+\angle y=\angle 2$ $[\because$exterior angle is equals to sum of two opposite interior angles]

$\Rightarrow \angle z+100°=150°$

$\Rightarrow \angle z=150°-100°$

$\Rightarrow \angle z=50°$

Hence the values of is $\angle x,\angle y,and\angle z$ are $80°,100°and50°$ respectively.