Question

Find x and y

can someone pls help

Answer 1

x = 25, y = 10

Explanation:

I'll add a drawing of my own so that it's easier for me to explain, and for you to understand.

Since line BC and line DE are parallel and line AE is being shared, angle ACB and angle CED will be the same. So the square will also be 3y.

Since line AB and line CD are parallel and line AE is being shared, angle CAB and angle ECD will be the same. So the heart will be 2x.

Now that we figured out two unknown angles, we can see that the two triangles share two angles with the same value. Since angles in a triangle add up to 180 (Added angles in every triangle are the same), the triangle shape (I drew) will be 4x.

We have a few clues to find the value of x and y.

1) 2x + 4x + 3y = 180 (all angles in a triangle add up to 180)

2) 3y + 2x = 180 - 100 (If you look near point C, we can see that 3y + 100 + 2x equals a flat line. A flat line equals 180)

We can use substitution. 3y + 2x can be replaced with 80.

So our new equation will be: 4x = 100

x = 25.

Now we can replace x with 25 in our second clue.

3y + 2(25) = 80

3y + 50 = 80

3y = 30

y = 10.

We can conclude that x = 25, and y = 10

Answer 2

x = 25 and y = 10

Explanation:

The arrows on the line segments mean the lines are parallel.

Therefore, the diagram shows two similar triangles, which means their interior angles are the same size. (Refer to the attached diagram).

Interior angles of a triangle sum to 180°:

⇒ 2x + 4x + 3y = 180

⇒ 6x + 3y = 180

⇒ 3(2x + y) = 180

⇒ 2x + y = 60

⇒ 2x = 60 - y

Angles on a straight line sum to 180°:

⇒ 3y + 100 + 2x = 180

⇒ 2x + 3y = 80

⇒ 2x = 80 - 3y

Substitute the first equation into the second equation, and solve for y:

⇒ 60 - y = 80 - 3y

⇒ 60 + 2y = 80

⇒ 2y = 20

⇒ y = 10

Substitute the found value of y into one of the equations and solve for x:

⇒ 2x = 60 - 10

⇒ 2x = 50

⇒ x = 25

Therefore, x = 25 and y = 10.