Question

in figure find X and Y if angle ACB =100 , and angle ADE = 120

Answer 1

$\textsf{Hey !!..}$

The answer goes here....

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》To find -

$x$ & $y$

》Given -

$\angle ACB$ = 100°

$\angle ADE$ = 120°

》Solution -

In order to find the angles $x$ & $y$ , we need to use some certain properties of the triangle.

We know that sum of the angles of a linear pair is always equal to 180°.

So, $\angle ACB$ and $x$ are linear pairs.

Therefore,

⇒ $\angle ACB+x$ = 180°

⇒ 100°$+x$ = 180°

⇒ $x$ = 180°$-$100°

⇒ $x$ = 80°

So, $x$ is equal to 80°.

Same applies to $\angle ADC$ -

⇒ $\angle ADC+\angle ADE$ = 180°

⇒ $\angle ADC+$120° = 180°

⇒ $\angle ADC$ = 180°$-$120°

⇒ $\angle ADC$ = 60°

So, $\angle ADC$ is equal to 60°.

Also, we know that sum of all the angles of a triangle is equal to 180°.

So, in $\triangle ACD$ -

⇒ $x+y+\angle ADC$ = 180°

⇒ 80°$+y+$60° = 180°

⇒ $y+$140° = 180°

⇒ $y$ = 180°$-$140°

⇒ $y$ = 40°

So, $y$ is equal to 40°.

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Thanks !!..

Answer 2

★$\bold{Heya...!!}$
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Here's your answer ...
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$\underline{Given:- }$

Angle ACB =100°

Angle ADE = 120°

To find :- x and y
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•°•From the given Figure , we can conclude that

•°•Angle ACB and angle ACD is making a linear pair.

And as we know that ,

Linear pair = 180°

so,

Angle ACB + Angle ACD = 180°

100°+ x = 180°

x = 180° - 100°

x = 80°

Here , we got the value of x(angle ACD) I.e 80°

Now,

Angle ADE = 120°( exterior angle)

As we know that An exterior angle of a triangle is equal to the sum of its opposite angles

so,

angle ADE = angle ACD + angle CAD

120 ° = 80° + y

120° - 80° = y

40°. = y

so, Here we got the value of y (angle CAD ) = 40 °

HENCE ,

x = 80°

y=40°

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$\bf{Thanks..!!}$