WXYZ is a parallelogram. WOZ = 110 WZO=36 and OZY=44° Find WXY
and a, b and c.
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Answers
Answer: - ∠a = 66°
∠b = 34°
∠c = 44°
∠WXY = 80°
Detailed answer: -
Given: -
∠WOZ = 110°
∠WZO = 36°
∠OZY = 44°
We need to find ∠WXY, ∠a, ∠b and ∠c.
WZ and XY lines are parallel to each other and WY and XZ are its transversal and also intersect each other at O.
So,
∠c = ∠OZY or we can write ∠XZY
i.e.,
∠c = 44° (alternate interior opposite angles)
Same way ∠ZXY = ∠XZW
i.e., ∠ZXY = 36° (alternate interior opposite angles)
Now, in Triangle OZW
∠Z = 36°
∠O = 110°
We need to find ∠W
We know that the sum of the angles of a given triangle is always = 180°
So,
Therefore,
∠Z + ∠O + ∠W = 180°
36° + 110° + ∠W = 180°
146° + ∠W = 180°
∠W = 180° - 146°
∠W = 34°
∠b = ∠YWZ = 34° (alternate interior opposite angles)
Now again in Triangle ZOY
∠z = 44°
∠O = ∠WOY - ∠WOZ
∠O = 180° - 110°
∠O = 70° (WOY is a straight line and so ∠WOY = 180°)
Now we need to find ∠a or ∠Y
The sum of all the angles of a triangle = 180°
Therefore,
i.e.,
∠Z + ∠O + ∠Y = 180°
44° + 70° +∠Y = 180°
114° + ∠Y = 180°
∠Y = 180° - 114°
∠Y = 66°
Therefore,
∠a = 66°
and
∠WXY = ∠WXZ + ∠ZXY
∠WXY = 44° + 36°
∠WXY = 80°
To know more about the topic, go to the following links: -
https://brainly.in/question/35634378
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