Question

1. classify the triangle by its angles and sides.

angles: (lower case answers)
sides: (lower case answers)

Explanation:

Step1: Calculate the third angle

The sum of angles in a triangle is \(180^\circ\). Given two angles \(40^\circ\) and \(25^\circ\), the third angle \(x = 180^\circ-(40^\circ + 25^\circ)=115^\circ\).

Step2: Classify by angles

A triangle with one angle greater than \(90^\circ\) (obtuse angle) is an obtuse triangle. Here, \(115^\circ>90^\circ\), so by angles, it's obtuse.

Step3: Classify by sides

Since all angles are of different measures, the sides opposite them will be of different lengths (by the Law of Sines), so it's a scalene triangle (no equal sides).

Answer:

Angles: obtuse
Sides: scalene