Question

In Fig. if $ AB\parallel CD$, $ \angle APQ=50°$ and $ \angle PRD=127°$, find $ x$ and $ y$.

50° 127° 

Answer 1

Step 1: To find the value of angle $x$.

Given: In the figure, we have

$AB\parallel CD$ and $PQ$ is a transversal

Now, $\angle APQ=\angle PQR$ [Alternate interior angles]

$\Rightarrow x=50°\mathbf{}\mathbf{[}\mathbf{\because }\mathbf{}\mathbf{\angle }\mathbf{APQ}\mathbf{=}\mathbf{50}\mathbf{°}\mathbf{]}$

Step 2: To find the value of angle $y$.

Again, $AB\parallel CD$ and $PR$ is a transversal

$\Rightarrow \angle APR=\angle PRD$ [Alternate interior angles]

$$\begin{gathered} \Rightarrow \angle APR=127°[\because ,\angle PRD=127°] \\ \Rightarrow 50°+y=127°[\because ,\angle APQ=50°] \\ \Rightarrow y=127°-50° \\ \Rightarrow y=77° \end{gathered}$$

Hence, the required angles are $x=50°$ and $y=77°$.