Question

answeronly if you know.....
make sure your answer is:-

$x = 35degrees \\ y = 70degrees \\ z = 75degrees$
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Answer 1

Answer :-

x = 35°

y = 70°

z = 75°

Step by step explanation :-

Given :-

• AB ║ CD
• ∠A = 75°
• ∠C = 35°

To Find :-

Value of x, y and z

Solution :-

In ΔDOC,

∠A = ∠D ( Alternate interior angles )

∠D = 75°

.·. z = 75°

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In ΔDOC,

∠C + ∠D + y = 180° ( By angle sum property )

35° + 75° + y = 180

110 + y = 180

y = 180 - 110

y = 70°

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∠DOC = ∠AOB ( Vertically opposite angles )

∠AOB = 70°

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In ΔAOB,

∠A + ∠O + x = 180° ( By angle sum property )

75° + 70 + x + 180

145 + x = 180

x = 180 - 145

x = 35°

Answer 2

$\huge\mathfrak\red{Answer:-}$

It is given that AB||CD , angle A =75° and angle C = 35°

We need to find the value of x, y and z.

Now,

In ∆ODC,

<A = <D [Alternate interior angles]

But, <D = 75°

=> z = 75°

Now by angle sum property of a triangle:

<C + <D + y = 180°

35° + 75° + y= 180°

110° + y = 180°

y= 180° - 110°

=> y = 70°

<DOC= <AOB [vertically opposite angles]

But <AOB = 70°

In ∆AOB

<A+ <O + x = 180°[angle sum property of a ∆]

75° + 70° + x = 180°

145° + x= 180°

x= 180° - 145°

=> x = 35°