Question

An isosceles triangle has three angles: x, x, and y

x + x + y = 180°
y = -2x + 180°
If x and y were equal, the triangle would be equilateral. How does your graph show this?​

Answer 1

To visualize the relationship between x and y in the given system of equations, we can plot them on a graph.

First, let's simplify the system of equations by substituting the second equation into the first one:

x + x + (-2x + 180°) = 180°

Simplifying this equation gives:

x = 60°

So we have found that one of the angles of the isosceles triangle is 60°.

Now, let's plot the equation y = -2x + 180° on a graph. This is a linear equation, which means that it will graph as a straight line.

To plot the line, we can find two points on it. When x = 0, y = 180°, and when x = 90°, y = 0. Plotting these two points and drawing a line through them

The line represents the equation y = -2x + 180°.

To see how the graph shows that an equilateral triangle is formed when x = y, we can add another line to the graph representing the equation y = x. This line represents the case where x = y, which corresponds to an equilateral triangle.

Another line in the graph below represents the equation y = x

We can see that the line intersects the first line at a point where x = 60°, which is the angle we found earlier. This means that when x = y = 60°, the isosceles triangle becomes equilateral.