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In the figure above,AD intersects BE at C. If x=100 , what is the value of y?

A) 100

B) 60

C) 90

D) 80

Answer:

The answer is D), 80.

Step-by-step explanation:

All sides of a triangle must add up to 180°. So, if x = 100, angle BCA must equal 60° because 180 - 120 = 60. Since angles BCA and DCE are vertical angles, they are equal, making angles DCE 60°. All you need to do now is add up 60 + 40; that should give you 100. You also need to subtract that from 180 to get your final answer of y = 80°.

The solution is Option D.

The value of y from the two triangles is given by the equation y = 80°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the first triangle be represented as ABC

Now , let the second triangle be represented as CDE

Now ,

The measure of angle x = 100°

The measure of ∠ACB = measure of ∠DCE ( vertically opposite angles )

And , for a triangle ∠A + ∠B + ∠C = 180°

So , The measure of ∠ACB  = 180° - ( x° + 20° )

And , the measure of ∠DCE = 180° - ( y° + 40° )

Substituting the values in the equation , we get

180° - ( x° + 20° ) = 180° - ( y° + 40° )

when x = 100°

Subtracting 180° on both sides of the equation , we get

- ( x° + 20° ) = - ( y° + 40° )

( 100° + 20 ) = ( y° + 40° )

( y° + 40° ) = 120°

Subtracting 40° on both sides of the equation , we get

y = 80°

Hence , the measure of angle ∠y = 80°

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