Classifying Triangles — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. A triangle has angles of 60 and 70 degrees. What is the third angle?
A) 30 degrees
B) 40 degrees
C) 50 degrees
D) 60 degrees
180 minus 60 minus 70 equals 50, so the third angle is 50 degrees.
2. Which set of angles could form a triangle?
A) 80, 60, 50 degrees
B) 100, 50, 40 degrees
C) 60, 60, 60 degrees
D) 90, 90, 10 degrees
60 plus 60 plus 60 equals 180, so those angles form a triangle; the others do not add to 180.
3. A triangle has angles of 90, 45, and 45 degrees. How would you classify it?
A) Right scalene
B) Acute equilateral
C) Right isosceles
D) Obtuse isosceles
The 90 degree angle makes it right, and the two equal 45 degree angles mean two equal sides, so it is right isosceles.
4. A triangle has sides 6 cm, 6 cm, and 6 cm. Which classification is always correct?
A) Right equilateral
B) Acute equilateral
C) Obtuse scalene
D) Right isosceles
An equilateral triangle has three 60 degree angles, all less than 90 degrees, so it is always acute equilateral.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A triangle has angles 35 and 95 degrees. The third angle is 50 degrees.
180 minus 35 minus 95 equals 50, so the third angle is 50 degrees.
2. A triangle with angles 30, 60, and 90 degrees is a right scalene triangle by sides.
Because each angle is a different size, each opposite side is a different length, making it scalene.
3. A triangle has angles 20, 20, and 140 degrees, making it an obtuse isosceles triangle.
180 minus 20 minus 20 equals 140; the 140 degree angle is obtuse and two equal angles make it isosceles.
4. If a triangle has two 50 degree angles, the third angle is 80 degrees.
180 minus 50 minus 50 equals 80, so the third angle is 80 degrees and the triangle is acute isosceles.
5. A triangle cannot have two 90 degree angles, because the three angles must add to 180 degrees.
Two 90 degree angles already sum to 180 degrees, leaving 0 degrees for the third angle, which is not possible.