Remember that each triangle needs to have the sum of interior angle measures equal to 180^(∘).
Never
Practice makes perfect
We want to determine whether the given statement is always, sometimes or never true.
A triangle has more than one vertex with an acute exterior angle.
Recall that the measure of an exterior angle of a triangle equals the sum of the measures of 2 nonadjacent interior angles. Because in each triangle the sum of interior angle measures needs to be equal to 180^(∘), this means that an exterior angle and its adjacent interior angle are supplementary angles. Let's take a look at the example!
When an exterior angle is acute, its adjacent interior angle needs to be obtuse because they add up to 180^(∘). This means that if we want a triangle to have more than one acute exterior angle, then it would need to have more than one obtuse angle. Let's imagine that we are given three sets of angle measures.
Set of Angle Measures
Sum of the Angle Measures
Can We Construct a Triangle?
1^(∘), 91^(∘), and 91^(∘)
183^(∘) > 180^(∘)
No
28^(∘), 57^(∘), and 95^(∘)
180^(∘) = 180^(∘)
Yes
10^(∘), 100^(∘), and 120^(∘)
230^(∘) > 180^(∘)
No
The sum of the angle measures in each and every triangle is equal 180^(∘). Therefore, it is impossible to have a triangle with more than one obtuse angle and, because of that, the given statement is never true.
