Triangle: Finding $x$ and $y$ (2 sides are given) - 6th grade

Question

I am helping my son with this homework and I was wondering if I can get a tip or few.

The question is: Write and solve equations to determine the values of $x$ and $y$. (see picture attached)

The triangle is $GKH$, $GK$ length is $(y+3.5)$cm and $KH$ length is $7.1$ cm. I can get $y$ from here since it's isosceles. The degree $\angle GHK$ is $1.5x$. I am not sure how to get degrees for each angle or the value of $x$.

Answer 1

You are given three lines on the sides of $\triangle GHK$. This notation is used to show that the sides are the same length.

This means that the triangle is an equilateral triangle. All of the interior angles in an equilateral triangle are $60^{\circ}$. This means

$$1.5x = 60$$

Since $\overline{HK} = 7.1 \,\text{cm}$, we also know that

$$\overline{GK} = y + 3.4 \,\text{cm} = 7.1 \,\text{cm}$$

Answer 2

Hint: The triangle is equilateral - what does this imply for its angles?

Also note that it is $(y+3.4)$ (at least in the picture) not $3.5$.

Answer 3

You have $(y + 3.5) = 7.1 \implies y = 3.6$. Also, as the triangle is equilateral all internal angels are the same and must add to 180 degrees, thus the equation: $3 \times 1.5x = 180 \implies 4.5x = 180 \implies x = 40$. This agrees with intuition, given each angle is 60 degrees, so $1.5 \times 40 = 60$ degrees.