Angles in Triangles
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Questions and Answers

What is the sum of interior angles in a triangle?

  • 120°
  • 240°
  • 360°
  • 180° (correct)
  • What type of angle has a measure between 0° and 90°?

  • Obtuse Angle
  • Right Angle
  • Straight Angle
  • Acute Angle (correct)
  • What is the measure of an exterior angle of a triangle equal to?

  • The sum of the measures of the two adjacent interior angles
  • The sum of the measures of all three interior angles
  • The difference of the measures of the two non-adjacent interior angles
  • The sum of the measures of the two non-adjacent interior angles (correct)
  • What type of angles have a sum of 90°?

    <p>Complementary Angles</p> Signup and view all the answers

    What type of angles are formed by two intersecting lines?

    <p>Vertical Angles</p> Signup and view all the answers

    What theorem states that if two triangles are similar, corresponding angles are equal?

    <p>Corresponding Angles Theorem</p> Signup and view all the answers

    Study Notes

    Angles in Triangles

    Angle Properties

    • The sum of interior angles in a triangle is always 180°.
    • The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

    Types of Angles

    • Acute Angle: An angle whose measure is between 0° and 90°.
    • Right Angle: An angle whose measure is 90°.
    • Obtuse Angle: An angle whose measure is between 90° and 180°.
    • Straight Angle: An angle whose measure is 180°.

    Angle Relationships

    • Complementary Angles: Two angles whose sum is 90°.
    • Supplementary Angles: Two angles whose sum is 180°.
    • Vertical Angles: Two angles formed by two intersecting lines, always equal in measure.

    Angle Theorems

    • Angle Sum Theorem: The sum of interior angles in a triangle is always 180°.
    • Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
    • Corresponding Angles Theorem: If two triangles are similar, corresponding angles are equal.

    Angle Properties

    • The sum of interior angles in a triangle is always 180°, a fundamental property of triangles.
    • The measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles, a key relationship between interior and exterior angles.

    Types of Angles

    • Acute Angle: Defined as an angle with a measure between 0° and 90°, indicating a sharp or narrow angle.
    • Right Angle: A 90° angle, a fundamental angle in geometry and trigonometry.
    • Obtuse Angle: An angle with a measure between 90° and 180°, a wider angle than an acute angle.
    • Straight Angle: A 180° angle, essentially a straight line.

    Angle Relationships

    • Complementary Angles: Two angles with a sum of 90°, a key concept in trigonometry and geometry.
    • Supplementary Angles: Two angles with a sum of 180°, another important relationship between angles.
    • Vertical Angles: Two angles formed by two intersecting lines, always equal in measure, a fundamental concept in geometry.

    Angle Theorems

    • Angle Sum Theorem: The sum of interior angles in a triangle is always 180°, a foundational theorem in geometry.
    • Exterior Angle Theorem: The measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles, a key theorem in triangle geometry.
    • Corresponding Angles Theorem: If two triangles are similar, corresponding angles are equal, a crucial theorem in similar triangles.

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    Description

    Learn about the properties and types of angles in triangles, including acute, right, obtuse, and straight angles.

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