Geometry: Triangles Worksheet

Question 1

A triangle has angle measures of 40 degrees, 60 degrees, and 80 degrees. Classify the triangle by its angles.

Accepted Answer

The triangle is an acute triangle because all three angles are less than 90 degrees.

Question 2

A triangle has side lengths of 6 cm, 6 cm, and 9 cm. Classify the triangle by its sides.

Accepted Answer

The triangle is isosceles because it has exactly two sides with the same length.

Question 3

Two angles of a triangle measure 35 degrees and 75 degrees. Find the measure of the third angle.

Accepted Answer

The third angle measures 70 degrees because the angles in a triangle add to 180 degrees, and 180 - 35 - 75 = 70.

Question 4

A triangle has angle measures of 90 degrees, 30 degrees, and 60 degrees. Classify the triangle by its angles and by its sides if all side lengths are different.

Accepted Answer

The triangle is a right triangle because it has one 90 degree angle. It is also scalene because all three side lengths are different.

Question 5

Can side lengths of 4 cm, 7 cm, and 12 cm form a triangle? Explain your answer.

Accepted Answer

No, these side lengths cannot form a triangle because 4 + 7 = 11, and 11 is not greater than 12. The sum of the two shorter sides must be greater than the longest side.

Question 6

In triangle ABC, angle A measures 50 degrees and angle B measures 65 degrees. What is the measure of angle C?

Accepted Answer

Angle C measures 65 degrees because 180 - 50 - 65 = 65.

Question 7

A triangle has side lengths of 8 units, 8 units, and 8 units. Classify the triangle by its sides and explain what you know about its angles.

Accepted Answer

The triangle is equilateral because all three sides are equal. Each angle measures 60 degrees because an equilateral triangle has three equal angles that add to 180 degrees.

Question 8

A triangle has one angle that measures 115 degrees. What type of triangle is it by its angles?

Accepted Answer

The triangle is obtuse because it has one angle greater than 90 degrees.

Question 9

Find the value of x in a triangle with angles measuring x degrees, 45 degrees, and 55 degrees.

Accepted Answer

The value of x is 80 because x + 45 + 55 = 180, so x + 100 = 180 and x = 80.

Question 10

A triangle has side lengths of 5 inches, 12 inches, and 13 inches. Does it appear to be a right triangle? Use the Pythagorean relationship to explain.

Accepted Answer

Yes, it is a right triangle because 5 squared plus 12 squared equals 13 squared. Since 25 + 144 = 169, the side lengths satisfy the Pythagorean relationship.

Question 11

In the diagram, a triangle has two equal sides. The angle between the equal sides measures 40 degrees. What are the measures of the other two angles?

Accepted Answer

The other two angles each measure 70 degrees. The triangle is isosceles, so the two base angles are equal, and 180 - 40 = 140, then 140 divided by 2 = 70.

Question 12

The exterior angle of a triangle measures 120 degrees. The two remote interior angles are labeled 45 degrees and x degrees. Find x.

Accepted Answer

The value of x is 75 degrees because an exterior angle equals the sum of the two remote interior angles, so 45 + x = 120 and x = 75.

Question 13

Can a triangle have angle measures of 25 degrees, 65 degrees, and 100 degrees? Explain your answer.

Accepted Answer

No, these cannot be the angle measures of a triangle because 25 + 65 + 100 = 190, and the angles in a triangle must add to 180 degrees.

Question 14

A scalene triangle has sides labeled 7 cm, 10 cm, and 12 cm. Which angle is the largest: the angle opposite 7 cm, the angle opposite 10 cm, or the angle opposite 12 cm?

Accepted Answer

The angle opposite 12 cm is the largest because the largest angle in a triangle is always across from the longest side.

Question 15

A triangle is shown with angles labeled 2x degrees, 3x degrees, and 4x degrees. Find the value of x and the measure of each angle.

Accepted Answer

The value of x is 20 because 2x + 3x + 4x = 180, so 9x = 180 and x = 20. The angle measures are 40 degrees, 60 degrees, and 80 degrees.

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Geometry: Triangles

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