Question

The Firgure shows two parallel lines AB and CD cut by transversals EF and GH. Angle EKD measures 90 degrees. What is the measure of angle x?A) 40 degrees B) 45 degrees C) 50 degrees D) 55 degrees

Answer 1

Option D is correct.

x = 55 degrees

Step-by-step explanation

From the image attached, we can see that Angle EKG = 35° and we've been told in the question that Angle EKD = 90°.

So, from the figure again, we can see that

(Angle EKG) + (Angle GKD) = Angle EKD

Angle EKG = 35°

Angle GKD = ?

Angle EKD = 90°

(Angle EKG) + (Angle GKD) = Angle EKD

35° + Angle GKD = 90°

Angle GKD = 90° - 35°

Angle GKD = 55°

Then, to find x, we will use the concept of corresponding angles.

Corresponding angles are angles that occupy similar positions on two different lines connected by another straight line (called the transversal line). If the lines are parallel to each other, then corresponding angles are equal to each other.

From the image, we can see that

x = Angle GKD (Corresponding angles are equal)

Hence,

x = Angle GKD = 55°

Hope this Helps!!!