We want to determine whether we can construct one, many, or notriangles that have one angle measure of 20^(∘), one angle measure of 35^(∘), and a side length of 3 inches between the two angles. First, we can use a ruler to draw a 3-inch side of our triangle.
To find the position of the third vertex, we can begin by drawing an angle of 20^(∘) using a protractor. Let's call the vertex of this angle A.
Now we can draw the 35^(∘) angle with its vertex at the other point of the 3-inch side of our triangle. We can call this vertex B.
The third vertex of our triangle is the point of intersection between the two rays. We can denote the vertex with C. Finally, we can draw a triangle with the given measures.
We know that the sum of angle measures in a triangle is 180^(∘). This means that the third angle measure in our triangle is always the same. In this case, there is only one triangle that has the given description.
