# What’s the value of x and y?

### 6 Answers

- RRLv 710 months agoFavorite Answer
You can work it out, step by step:

The triangle on the right is an equilateral triangle, so all angles are 60 degrees

The left hand triangle is an isosceles triangle. Its peak is 180 - 60 = 120 degrees (supplementary angle of 60 degrees)

The other two angles in the isosceles triangle will be equal and will total 180 -120 = 60. Each one will be 60/2 = 30 degrees

Now you have two simple equations:

7y + 9 = 30

7y = 21

y = 3

4x - 2 = 30

4x = 32

x = 8

- la consoleLv 710 months ago
The triangle at the right side is an equilateral triangle, so its 3 angles are equal.

blue = green = red = 60 °

You can see that:

red + yellow = 180

yellow = 180 - red

yellow = 120

Whatever the triangle, the sum of the 3 angles is always 180 °.

(4x - 2) + (7y + 9) + yellow = 180

(4x - 2) + (7y + 9) = 180 - yellow

(4x - 2) + (7y + 9) = 60 → as the triangle at the left side, is an isosceles triangle: (7y + 9) = (4x - 2)

(4x - 2) + (4x - 2) = 60

2.(4x - 2) = 60

4x - 2 = 30

4x = 32

→ x = 8

Recall: (7y + 9) = (4x - 2)

7y + 9 = 32 - 2

7y = 21

→ y = 3

- DavidLv 710 months ago
Both base angles of the isosceles triangle are 30 degrees;

If 4x - 2 = 30 then x = 8

If 7y + 9 = 30 then y = 3

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- sepiaLv 710 months ago
120 + (4x - 2) + (7y + 9) = 180

4x + 7y = 53

4x - 2 = 30

x = 8

7y + 9 = 180 - 120 - 30

y = 3