We can draw a triangle between Jamestown, Williamsburg, and Yorktown. Let's look at the map!
We are given that the interior angle at Williamsburg ∠ W measures 120^(∘) and that the interior angle at Jamestown ∠ J is twice the measure of the angle at Yorktown ∠ Y. We can write the measurements for ∠ J and ∠ Y in terms of the variable x using the given relationship.
m∠ W = 120^(∘) , m∠ J= 2x^(∘) , and
m∠ Y = x^(∘)
Recall that interior angles of a triangle are the angles inside that triangle. With this information, we can mark the angles ∠ W, ∠ J, and ∠ Y on the diagram.
Next, we can find the measure of the interior angles at Jamestown and Yorktown. We will do this using the rule for the interior angle measures of a triangle.
Interior Angle Measures of a Triangle
The sum of the interior angles of a triangle is 180^(∘).
Using this rule, we can write the equation for the interior angles of the given triangle.
120^(∘) + 2x^(∘)+ x^(∘)=180^(∘)
Now, let's solve the equation for x.
We found that x=20. This means that the measure of interior angle at Yorktown is 20^(∘). We can substitute 20 for x to evaluate the expression for the interior angle at Jamestown.
