Exercise 23 Page 210

We want to find the measures of the angles in a isosceles triangle by creating a system of linear equations and solving it. Let's take a look at the given diagram.

From the exercise, we know that the measure of the obtuse angle y is two and a half times the measure of one of the acute angles x. We can use this information to create the first equation. y=2.5xNext, let's recall an important property about the interior angles of a triangle.

With this in mind, let's write a second equation about the angle measures in our triangle. 2x+y=180 Now we can combine both equations and create the system of equations. y=2.5x & (I) 2x+y=180 & (II) Next, let's solve this system using the Substitution Method. Notice that Equation (I) is already solved for y. Because of this, we will substitute 2.5x for y in Equation (II) and solve it for x.

Now that we have a value for x, we can substitute its value for x in either equation and solve for y. Let's substitute 40 for x in Equation (I) for simplicity.

We found that the measure of the obtuse angle in the given triangle is 100^(∘) and the measure of the acute angles is 40^(∘).