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Triangle Word Problems Practice Questions

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Updated on Oct 4, 2011

To review these concepts, go to Triangle Word Problems Study Guide.

Triangle Word Problems Practice Questions

Practice 1

Problems

  1. In an acute triangle, the measures of two angles are 50° and 60°. What is the measure of the third angle?
  2. In an obtuse triangle, the measures of two angles are 120° and 10°. What is the measure of the third angle?
  3. One acute angle of a right triangle measures 35°. What is the measure of the other acute angle?

Solutions

  1. Read and understand the question. This question is looking for the measure of the third angle of a triangle where the measures of two angles are given.
  2. Make a plan. The triangle is acute, so the result will be an angle with a measure less than 90°. Add the measures of the two known angles, and subtract the sum from 180°.

    Carry out the plan. The sum of the two known angles is

      50 + 60 = 110
      180 – 110 = 70

    The measure of the third angle is 70°.

    Check your answer. To check this solution, add the three angles and make sure that the sum is 180°.

      50 + 60 + 70 = 180

    This solution is checking.

  3. Read and understand the question. This question is looking for the measure of the third angle of an obtuse triangle when two angles are given.
  4. Make a plan. Add the two known angles and subtract this sum from 180°.

    Carry out the plan. First, add the two known angles: 120 + 10 = 130. Then, subtract this amount from the total of 180°: 180 – 130 = 50. The third angle is 50°.

    Check your answer. To check this solution, add the three angles to make sure that the sum is exactly 180°: 120 + 10 + 50 = 180°. This answer is checking.

  5. Read and understand the question. This question is asking for the measure of the third angle of a right triangle when one of the other acute angles is known.
  6. Make a plan. Add the two known angles and subtract this sum from 180°. Carry out the plan. Because the triangle is a right triangle, one of the other angles is 90°. Then, add the two known angles: 35 + 90 = 125. Finally, subtract this amount from the total of 180°: 180 – 125 = 55. The third angle is 55°.

    Check your answer. To check this solution, add the three angles to make sure that the sum is exactly 180°: 35 + 90 + 55 = 180°. This question is checking.

Practice 2

Problems

  1. In a scalene triangle, one side is 5 units more than twice the measure of the shortest side. The other side is three times the measure of the shortest side. If the sum of the three sides is 41 units, what is the measure of each side of the triangle?
  2. Two sides of an equilateral triangle measure x + 1 units and 2x – 10 units, respectively. What is the value of x?
  3. The two congruent sides of an isosceles triangle are represented by 2x – 5 units and x + 3 units. What is the length of each of these congruent sides?
  4. Two sides of a triangular garden measure 12 m and 15 m. Between what two values must the third side measure?
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