AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 59°. G is a point between AB and CD such that ∠BEG = 50° and ∠GFE = 33°. What is the measure of ∠EGF?​

Correct option is A

Given:

AB is parallel to CD.
A transversal PQ intersects AB and CD at E and F, respectively.
∠PEB = 59°.
G is a point between AB and CD such that:
∠BEG = 50°
∠GFE = 33°
We need to find the measure of ∠EGF.

Formula Used:
Sum of angles in a triangle = 180°.

Solution:

Using the linear pair on ∠PEB and ∠BEF:

​$$\angle PEB + \angle BEF = 180^\circ$$​​

$$59^\circ + \angle BEF = 180^\circ$$​​
​$$\angle BEF = 180^\circ - 59^\circ = 121^\circ$$​​

Now, at point E on line segment EF, $$\angle$$​ BEF splits into ($$\angle BEG + \angle GEF):$$​​
​$$\angle GEF = \angle BEF - \angle BEG = 121^\circ - 50^\circ = 71^\circ$$​​

In $$\triangle EGF$$​, apply the angle sum property:

​$$\angle GEF + \angle GFE + \angle EGF = 180^\circ \\ \ \\71^\circ + 33^\circ + \angle EGF = 180^\circ \\ \ \\\angle EGF = 180^\circ - 104^\circ = 76^\circ$$​​