Question

In the given figure, $$AB \parallel CD$$ and $$EF \perp AB$$. If $$EG$$ is the transversal such that $$\angle GED = 130^{\circ}$$, find $$\angle EGF$$.

Answer 1

We know that $$AB \parallel CD$$ and $$GE$$ is the transversal

From the figure we know that $$\angle EGF$$ and $$\angle GED$$ are interior angles

So we get

$$\angle EGF + \angle GED = 180^{\circ}$$

By substituting the values

$$\angle EGF + 130^{\circ} = 180^{\circ}$$

On further calculation

$$\angle EGF = 180^{\circ} - 130^{\circ}$$

By subtraction

$$\angle EGF = 50^{\circ}$$

Therefore, $$\angle EGF = 50^{\circ}$$.