Question

In the figure given below, find$\angle 1,\angle 2,\angle 3,\angle 4and\angle 5$

Answer 1

Given figure

In the given figure

Step 1: Find $\angle 5$

$\angle 5=140°(verticallyoppositeangle)$

Step 2: Find $\angle 2$

$$\begin{gathered} \angle 2+\angle 5=180°(bylinearpairaxiom) \\ \Rightarrow \angle 2+140°=180° \\ \Rightarrow \angle 2=180°-140°=40° \end{gathered}$$

Step 3: Find $\angle 1$

In $△CDE$

$$\begin{gathered} \angle 1+\angle 2+50°=180°(anglesumproperty) \\ \Rightarrow \angle 1+40°+50°=180° \\ \Rightarrow \angle 1+90°=180° \\ \Rightarrow \angle 1=180°-90°=90° \end{gathered}$$

Step 4:Find$\angle 3$

$\angle 3=\angle 2=40°(verticallyoppositeangle)$

Step 5: Find $\angle 4$

In $△ABC$

$$\begin{gathered} \angle 4+\angle 3+45°=180°(anglesumproperty) \\ \angle 4+40°+45°=180° \\ \angle 4+85°=180° \\ \angle 4=180°-85°=95° \end{gathered}$$

Hence, $\angle 1=90°,\angle 2=40°,\angle 3=40°,\angle 4=95°and\angle 5=140°$