Question

Select the correct answers.

A pair of parallel lines is cut by another pair of parallel line as shown in the figure. Which angles are congruent to angle K?


A - angles P, Q, and R

B - angles M, E, and C

C - angles G, A, and B

D - angles D, E, and C

E - angles M, N, and P

Answer 1

angles M,E,C are congruent to angle K

Explanation:

Answer 2

Option B is the right choice,congruent to
`\angle K` are
`\angle M,\angle E,\angle C`.

Explanation:

If we look on to the diagram and the options we can sort out the angles on the basis of our requirement.

There are three sets arising from the angles.

`\angle K=\angle P` [Corresponding angles]

The corresponding angles are the ones at the same location at each intersection.

`\angle K=\angle M` [Vertically opposite angles]

And

`\angle M=\angle P` [Alternate interior angles]

Now

`\angle R =\angle C =\angle E` [Corresponding angles]

`\angle C=\angle A` [Vertically opposite angles]

`\angle G=\angle E` [Vertically opposite angles]

`\angle K=\angle M=\angle P=\angle R=\angle C=\angle A=\angle E=\angle =\angle G`

So the correct pair from the options given is B which includes
`\angle M=\angle E=\angle C`