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Quadrilateral Word Problems Practice Questions

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Updated on Oct 3, 2011

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

Quadrilateral Word Problems Practice Questions

Practice 1

The following practice questions test your knowledge of the properties of quadrilaterals in general and parallelograms.

Problems

  1. One side of a square is 4 meters. What is the measure of each of the other sides?
  2. What is the value of x in the following figure?
  3. Parallelogram

  4. The measure of a side of a parallelogram is 24 inches. What is the measure of the side opposite from this side?
  5. The measure of one angle of a rhombus is 35°. What is the measure of a consecutive angle of that angle?

Solutions

  1. Every side of a square measures the same length. Each side is 4 m.
  2. In a parallelogram, the opposite angles are congruent. Thus, the value of x is 65°.
  3. In a parallelogram, the sides opposite each other are congruent. The measure of the opposite side is 24 inches.
  4. The measures of consecutive angles of a rhombus are supplementary, or equal to 180°. The measure of the consecutive angle is 180 – 35 = 145°.

Practice 2

This practice set will test your skills applying the properties of trapezoids.

Problems

  1. Three angles of a trapezoid measure 100°, 90°, and 75°. What is the measure of the other angle?
  2. The measure of a leg of an isosceles trapezoid is 14 feet. What is the measure of the other leg?
  3. The length of a diagonal of an isosceles trapezoid is 50 inches. What is the measure of the other diagonal?

Solutions

  1. To find the measure of the other angle, add the known angle measures together, and subtract the sum from 360°. The three known angles add to 100 + 90 + 75 = 265; 360 – 265 = 95. The missing angle is 95°.
  2. The legs of an isosceles trapezoid have the same length. The other leg measures 14 feet.
  3. The diagonals of an isosceles trapezoid are the same length. The measure of the other diagonal is 50 inches.

Practice 3

Use the steps to solving word problems and your knowledge of quadrilaterals to solve each of the questions in the following set.

Problems

  1. The angles of a quadrilateral are 65°, 95°, and 110°. What is the measure of the other angle?
  2. The measure of a diagonal of a square is represented by the expression 4x – 10. If the measure of the other diagonal is 10 meters, what is the value of x?
  3. The measures of two consecutive angles of a parallelogram are represented by the expressions 2x and 7x, respectively. What is the value of x?
  4. The opposite angles of a parallelogram are represented by the expressions x + 18 and 2x – 2, respectively. What is the measure of each angle?
  5. The measures of the base angles of an isosceles trapezoid are each 100°. What is the measure of each of the other angles in the figure?

Solutions

  1. Read and understand the question. This question is looking for the missing angle of a quadrilateral when three of the angle measures are given.
  2. Make a plan. Add the three known angle measures, and then subtract this amount from the total of 360° in the quadrilateral.

    Carry out the plan. To find the measure of the other angle, add the known angle measures together, and subtract the sum from 360°. The three known angles add to 65 + 95 + 110 = 270; 360 – 270 = 90. The missing angle is 90°.

    Check your answer. To check this result, add the four angles to be sure that the sum is 360° : 65 + 95 + 110 + 90 = 360, so this answer is checking.

  3. Read and understand the question. This question is looking for the value of x when information is given about the diagonals of a square.
  4. Make a plan. The lengths of the diagonals of a square are equal. Set the given expressions equal to each other, and solve for x.

    Carry out the plan. Set the expression equal to 10: 4x – 10 = 10. Add 10 to each side of the equation to get 4x = 20. Divide each side of the equation by 4 to get x = 5.

    Check your answer. To check this answer, substitute x = 5 into the expression 4x – 10 to be sure the value is 10.

      4(5) – 10 = 20 – 10 = 10

    This solution is checking.

  5. Read and understand the question. This question asks for the value of x when expressions for two consecutive angles of a parallelogram are given.
  6. Make a plan. Two consecutive angles of a parallelogram have a sum of 180°; they are supplementary. Add the two expressions, set the sum equal to 180, and solve for x.

    Carry out the plan. The equation becomes 2x + 7x = 180. Combine like terms to get 9x = 180. Divide each side of the equation by 9 to get x = 20.

    Check your answer. To check this solution, substitute the value of x into each expression. Then, add the two angle measures to be sure that the total is 180°. The angles are 2(20) = 40° and 7(20) = 140°. The sum of the angles is 40 + 140 = 180°. This result is checking.

  7. Read and understand the question. This question is looking for the measure of two opposite angles in a parallelogram.
  8. Make a plan. The measures of opposite angles of a parallelogram are equal.

    Set the given expressions equal to each other, and solve for x. Then, substitute the value of x into one of the expressions to find the measure of each angle.

    Carry out the plan. Set the expressions equal to each other: x + 18 = 2x – 2. Subtract x from each side of the equation to get 18 = x – 2. Add 2 to each side of the equation to get 20 = x. Substitute x = 20 into the expression x + 18.

      20 + 18 = 38

    The measure of each opposite angle is 38°.

    Check your answer. To check this answer, substitute x = 20 into the expression 2x – 2 to be sure the value is also 38.

      2(20) – 2 = 40 – 2 = 38

    This solution is checking.

  9. Read and understand the question. This question is looking for the measure of each of the unknown angles in an isosceles trapezoid. The measure of the base angles is given.
  10. Make a plan. Use the problem solving strategy of drawing a picture to help with this question. In an isosceles trapezoid, the two legs are congruent and the base angles are congruent. The following figure represents this trapezoid.

    Quadrilateral Word Problems

    Carry out the plan. The base angles of the trapezoid are congruent, so each of their measures is 100°. To find the measure of the other angles, subtract the sum of the base angles from 360 and divide the result by 2.

      360 – 300 = 160
      = 80

    degrees in each of the other angles. Thus, the angles measure 100, 100, 80, and 80°, respectively.

    Check your answer. To check this answer, add the measures of the four angles to be sure that the total number of degrees is 360.

      100 + 100 + 80 + 80 = 360°

    so this answer is checking.

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