Can anyone answer this ???
Answers
Step-by-step explanation:
Since ∠A and ∠D are co-interior angles, they will sum up to 180°.
∠A + ∠D = 180°
115° + ∠D = 180°
∠D = 180° - 115°
∠D = 65° or ∠x = 65°.
As ABCD is a parallelogram, opposite angles will be equal.
That is, ∠B = ∠D
Therefore, ∠B = 65°.
We see that BCE makes up a triangle.
So, all the angles would sum up to 180° because of the angle sum property of a triangle.
Therefore, 65° + 46° + m(the unknown angle) = 180°
111° + m = 180°
m = 180° - 111°
m = 69°.
By the figure, it is clear that ∠m and ∠z make up a linear pair angle and we know that, the sum of linear pair angles is always 180°.
Therefore, ∠m + ∠z = 180°
69° + ∠z = 180°
∠z = 180° - 69°
∠z = 111°.
We know that in a parallelogram, the opposite sides are parallel. So, AB is parallel to CD. Since BE is a part of AB, BE would also be parallel to CD.
By this, ∠z and ∠y become co-interior angles.
So, ∠z + ∠y = 180°
111° + ∠y = 180°
∠y = 180° - 111°
∠y = 69°.
So, the required angles, that are, x, y and z, measure 65°, 69° and 111°, respectively.
I hope it's clear! Please mark this answer as the BRAINLIEST.