Question - Finding the Value of an Angle in a Geometry Problem

In the given figure, AB is parallel to CD, and transversal EG intersects them, creating alternate interior angles.

Since AB || CD, angle EGP = angle EHG (alternate interior angles are equal).

Angle EHG = 85° (because it is given in the figure that angle EHP is 85°).

Hence, angle EGP also equals 85°.

Now, in triangle EGD:

Sum of angles in a triangle is 180°.

So, angle EGD + angle EGD + angle DEG = 180°.

115° + 85° + x = 180°.

200° + x = 180°.

x = 180° - 200°.

x = -20°.

However, an angle cannot be negative, and this result suggests a mistake in the given values or the interpretation of the diagram. Perhaps the diagram or its labels are not clearly represented or there is a typographical error in the angle measurements. In a valid geometrical context, all angles should be positive, and the sum of angles in a triangle must always be exactly 180°.