Exercise 24 Page 241

Consider △ UXZ. On this triangle, the measures of angles X and Z are both less than 90^(∘). Therefore, they are acute angles. Let's focus on ∠ U. This angle is cut in two parts by segment UY. The measure of the two parts are shown on the diagram.

Point Y is an inner point of angle ∠ UXZ, so we can use the Angle Addition Postulate.

m∠ XUZ=m∠ XUY+m∠ YUZ

SubstituteII

m∠ XUY= 60, m∠ YUZ= 20

m∠ XUZ= 60+ 20

AddTerms

Add terms

m∠ XUZ=80

The measure of the angle ∠ XUZ is also less than 90 ^(∘). Therefore, all of the angles are acute angles. With this information, we can conclude that △ UXZ is an acute triangle. Since not all of the angles have the same measure, this is an acute triangle that is not equiangular.