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Math Grade 4-5 Answer Key

Angles and Triangles

Classifying angles and identifying triangle types

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Angles and Triangles

Classifying angles and identifying triangle types

Math - Grade 4-5

Instructions: Read each problem carefully. Use what you know about angles and triangles to answer each question. Show your work when needed.
  1. 1

    An angle measures 35 degrees. Is it acute, right, or obtuse?

    Compare 35 degrees to 90 degrees.

    An angle that measures 35 degrees is acute because it is less than 90 degrees.
  2. 2

    An angle measures 90 degrees. Is it acute, right, or obtuse?

    An angle that measures 90 degrees is a right angle because right angles measure exactly 90 degrees.
  3. 3

    An angle measures 120 degrees. Is it acute, right, or obtuse?

    Obtuse angles are larger than right angles.

    An angle that measures 120 degrees is obtuse because it is greater than 90 degrees but less than 180 degrees.
  4. 4

    Draw one acute angle and label it with a measure that makes sense.

    A correct answer shows an angle less than 90 degrees, such as a 45 degree angle, and labels it clearly.
  5. 5

    Draw one right angle and label it with its measure.

    A right angle looks like the corner of a piece of paper.

    A correct answer shows a square corner shape and labels the angle as 90 degrees.
  6. 6

    Draw one obtuse angle and label it with a measure that makes sense.

    A correct answer shows an angle greater than 90 degrees and less than 180 degrees, such as 110 degrees, and labels it clearly.
  7. 7

    A triangle has 3 equal sides. What kind of triangle is it by its sides?

    The prefix equi means equal.

    A triangle with 3 equal sides is an equilateral triangle because all of its sides are the same length.
  8. 8

    A triangle has 2 equal sides and 1 side that is a different length. What kind of triangle is it by its sides?

    A triangle with 2 equal sides is an isosceles triangle because exactly two sides have the same length.
  9. 9

    A triangle has 3 sides of different lengths. What kind of triangle is it by its sides?

    Scalene means all side lengths are different.

    A triangle with 3 different side lengths is a scalene triangle because no sides are equal.
  10. 10

    A triangle has one right angle. What kind of triangle is it by its angles?

    A triangle with one right angle is a right triangle because one of its angles measures exactly 90 degrees.
  11. 11

    A triangle has three acute angles. What kind of triangle is it by its angles?

    Acute means less than 90 degrees.

    A triangle with three acute angles is an acute triangle because all of its angles are less than 90 degrees.
  12. 12

    A triangle has one obtuse angle. What kind of triangle is it by its angles?

    A triangle with one obtuse angle is an obtuse triangle because one angle is greater than 90 degrees.
  13. 13

    Can a triangle have two right angles? Explain why or why not.

    Add 90 degrees plus 90 degrees.

    No, a triangle cannot have two right angles because two right angles already add up to 180 degrees, and a triangle must have three angles that add up to 180 degrees total.
  14. 14

    Can a triangle have two obtuse angles? Explain why or why not.

    No, a triangle cannot have two obtuse angles because each obtuse angle is greater than 90 degrees, so two obtuse angles would add to more than 180 degrees.
  15. 15

    A triangle has side lengths 5 cm, 5 cm, and 8 cm. Classify the triangle by its sides.

    Look for sides that match.

    This triangle is isosceles because it has two equal side lengths, 5 cm and 5 cm.
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