Exercise 15 Page 132

We are given a triangle and asked to find the measure of the exterior angle. Let's first label the exterior angle as b.

First, we need to find the interior angles. Let's recall a key piece of information!

With this rule, we can write an equation connecting the expressions of the angles of our triangle. t^(∘)+ (t+10)^(∘)+ (t+20)^(∘)=180^(∘) Let's solve the equation and find the value of t. For simplicity, we will not write the degree symbol.

The measure of one of the angles is 50^(∘). To find the others missing measures, we will substitute t= 50 in the expressions for the remaining angles, (x+10)^(∘) and (t+20). Once again, we will remove the degree symbol for the calculation.

Let's add this information to our diagram.

Now, we will find the meausre of the exterior angle. let's recall the Exterior Angle Measures of a Triangle Theorem.

We will now identify the exterior angle and the two nonadjacent interior angles.

We can see that the measure of the exterior angle is b^(∘) and the measures of the nonadjacent interior angles are 50^(∘) and 60^(∘). By the Exterior Angle Measures of a Triangle Theorem, we can write an equation in terms of b. b^(∘)= 50^(∘)+ 60^(∘) Let's solve the equation! For simplicity, we will not write the degree symbol while solving.

The measure of the exterior angle is 110^(∘).