Question

in the following figure DPSE and KLMN are parallelograms. find the angle x​

Answer 1

Answer:

The angle x is acute angle

Step-by-step explanation:

hope it will help you please please mark as brainliest answer

Answer 2

Answer:

50°

Step-by-step explanation:

[Please refer to figure attached. I have made slight modifications for you to understand better]

Given,

DPSE and KLMN are parallelograms.

∠D = 120°

∠M = 70°

[Let the intersecting point be O]

∠KOP = x

Now in parallelogram DPSE, ∠P is adjacent to ∠D.

In a parallelogram, the adjacent angles are supplementary to each other.

So, ∠P + ∠D = 180°

=> ∠P + 120° = 180° [from given data]

=> ∠P = 180° - 120° = 60°.............................................[equation 1]

Similarly in parallelogram KLMN, ∠K is opposite to ∠M.

In a parallelogram, the opposite angles are equal.

So, ∠K = ∠M

∠M = 70° [from given data]

So,

∠K = 70°.............................................[equation 2]

Now, consider Δ OPK

By angle sum property, ∠OKP + ∠OPK + ∠KOP = 180°

From equations 1 and 2 and given data,

70° + 60° + x = 180°

=> x = 180° - (60° + 70°)

=> x = 180° - 130° = 50°