Question

In the given figure, line 11| line $m$ and line $n\parallel$ line $p$. Find $\angle a,\angle b,\angle c$ from the given measure of an angle.

Answer 1

i. consider $\angle d$ as shown in the figure line I $\parallel$ line $m$, and line $p$ is their transversal. $\therefore \angle d={45}^{\circ }$ [Corresponding angles]

Now, $\angle d+\angle b={180}^{\circ }$ [Angles in a linear pair]
$$\begin{array}{cc}& \therefore {45}^{\circ }+\angle b={180}^{\circ }\\ & \therefore \angle b={180}^{\circ }-{45}^{\circ }\\ & \therefore \angle b={135}^{\circ }\dots ..\text{(i)}\end{array}$$
ii. $\angle a=\angle$ b [Vertically opposite angles]
$\therefore \angle a={135}^{\circ }$ [From (i)]
iii. line $n\parallel$ line $p$, and line $m$ is their transversal.
$\therefore \angle C=\angle b$ [Corresponding angles]
$\therefore \angle C={135}^{\circ }\left[From\right(i\left)\right]$