Question

Joey says that triangle XYZ is obtuse. Robin disagrees because there are more acute angles then there are obtuse angles, therefore, it must be acute. Is either one of them correct? Explain your reasoning.

Answer 1

Joey is right: the triangle shown is obtuse

Explanation:

Remember the following definitions:

Acute angles are those that measure less than 90 °

The obtuse angles are those that measure more than 90 °.

The obtuse triangles are those with one obtuse angle and two acute angles

The acute triangles have three acute angles.

The triangle shown in the figure has one obtuse angle (Z = 138 °) and two acute angles (X = 27 °, y = 15 °)

So Joey is right: the triangle shown is obtuse

Answer 2

Robin is correct because angle XYZ is an acute angle.

Explanation:

An acute angle is one that has an angle value less than 90°.

Angle XYZ is 15° hence it fits this definition.

An Obtuse angle is one that has an angle value more than 90° but less than 180°. Angle XZY is 138° hence it fits this definition.

However, angle ZXY is also acute angle because it has an angle value of 27°