Question

Find the unknown angle x and y in each of the following figures...plz give answer in step by step explanation...correct answer will be marked BRAINLIEST and be followed...✌

Answer 1

Step-by-step explanation:

Let the point where the diagonals bisect Be O.

Since ZY || WX,

Angle ZYW = Angle YWX = 28° ( Alternate interior angles)

In Triangle OWX,

Angle OWX + Angle OXW + x = 180°

(Angle sum property of a Triangle)

=> 28° + 40° + x = 180°

=> 68° + x = 180°

=> x = 180°- 68°

=> x = 112°

Since ZW || YX,

Now, Angle ZWY = WYX = 43° (Alternate Interior angles)

So, y + Angle ZWY + Angle OWX = 180°

{Linear Pair}

=> y + 43° + 28° = 180°

=> y = 180° - (43° + 28°)

=> y = 180° - 71°

=> y = 109°

Therefore x = 112° and y = 109°

Answer 2

Answer:

x = 112° and y = 109°

Step-by-step explanation:

LET THE MIDDLE POINT BE O.

SINCE ZY//WX, ∠ZYX +∠YXW = 180°

                          ⇒ 28° + 43° + 40° + ∠ZXY = 180°

                          ⇒ ∠ZXY = 180° - 111° =69°

IN ΔXOY, ∠XOY + ∠ OYX +∠YXO = 180°

                   ⇒∠XOY = 180° - (43 + 69)° = 180° - 112° = 68°

WOY IS A STRAIGHT LINE, SO,   x +68° = 180° ⇒ x = 112°

SINCE ZW//YX,  y = ∠YXW = 40° + 69° = 109°