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Lines and Angles: Adjacent Angles, Angle Measures, Complementary and Supplementary Angles
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Lines and Angles: Adjacent Angles, Angle Measures, Complementary and Supplementary Angles

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Questions and Answers

Can two obtuse angles form a linear pair?

  • Not sure
  • Depends on the sizes of the angles
  • Yes
  • No (correct)
  • Which pair of angles below form a linear pair?

  • 65° and 90° (correct)
  • 80° and 100°
  • No pair forms a linear pair
  • 60° and 40°
  • What type of angles are ∠1 and ∠3 in relation to each other?

  • Linear pair angles
  • Supplementary angles
  • Vertically opposite angles (correct)
  • Complementary angles
  • If ∠1 is 70 degrees, what is the measure of ∠3?

    <p>70 degrees</p> Signup and view all the answers

    When two lines intersect, what kind of angles are ∠1 and ∠2?

    <p>Vertically opposite angles</p> Signup and view all the answers

    What happens when you rotate a copy of the figure by 180 degrees after fixing it at the point of intersection?

    <p>The lines overlap perfectly on top of each other.</p> Signup and view all the answers

    Which of the following pairs of angles are vertically opposite angles?

    <p>(∠COB, ∠AOD)</p> Signup and view all the answers

    What is the complement of a 40º angle?

    <p>60º</p> Signup and view all the answers

    In the figure, if ∠1 and ∠2 are supplementary and ∠1 is decreased, what should happen to ∠2 for them to remain supplementary?

    <p>Increase</p> Signup and view all the answers

    Can two obtuse angles be supplementary?

    <p>Yes</p> Signup and view all the answers

    If an angle is greater than 45º, what can be said about its complementary angle?

    <p>Less than 45º</p> Signup and view all the answers

    In the figure, which pair of angles forms a linear pair?

    <p>(∠COB, ∠BOD)</p> Signup and view all the answers

    If two angles are complementary, what is the sum of their measures?

    <p>90 degrees</p> Signup and view all the answers

    What do two angles form if their sum is 180 degrees?

    <p>Linear pair</p> Signup and view all the answers

    In a linear pair of angles, what is the total measure of the two angles?

    <p>180 degrees</p> Signup and view all the answers

    What do two adjacent supplementary angles form?

    <p>Linear pair</p> Signup and view all the answers

    In a figure where two lines intersect at a point, what are vertically opposite angles?

    <p>Equal</p> Signup and view all the answers

    If one pair of vertically opposite angles at an intersection point are acute, what are the other pair?

    <p>Obtuse</p> Signup and view all the answers

    In the context of parallel lines and transversals, what do alternate interior angles have in common?

    <p>They lie between the two lines</p> Signup and view all the answers

    What distinguishes corresponding angles from other angle pairs?

    <p>They are in 'corresponding' positions relative to the two lines</p> Signup and view all the answers

    Which type of angle pairs have the property of having different vertices and being in 'corresponding' positions?

    <p>Pairs of corresponding angles</p> Signup and view all the answers

    What is a key characteristic of exterior angles formed by a transversal with parallel lines?

    <p>They add up to 180 degrees</p> Signup and view all the answers

    Which statement best describes pairs of alternate exterior angles?

    <p>They are on opposite sides of the transversal and have different vertices</p> Signup and view all the answers

    When drawing a transversal to parallel lines, what should be true about the alternate interior angles created?

    <p>They should have different vertices</p> Signup and view all the answers

    What do we call angles that have a common vertex and a common arm but no common interior?

    <p>Adjacent angles</p> Signup and view all the answers

    What type of angles are equal in measure when two lines intersect?

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

    What relationship is observed between the angles ∠1 and ∠5 when a transversal cuts two parallel lines?

    <p>They are corresponding angles</p> Signup and view all the answers

    What type of angles are ∠3 and ∠6 in relation to each other?

    <p>Alternate interior angles</p> Signup and view all the answers

    What do we call the meeting point of two lines when they intersect?

    <p>Intersection point</p> Signup and view all the answers

    Which type of angles are ∠4 and ∠5 in relation to each other when two lines intersect?

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

    Study Notes

    Angle Relationships

    • Two obtuse angles cannot form a linear pair.
    • When two lines intersect, they form a linear pair, and the angles are supplementary.

    Linear Pairs

    • ∠1 and ∠2 form a linear pair, and their sum is 180 degrees.
    • If ∠1 is 70 degrees, then ∠3 is 110 degrees.

    Vertically Opposite Angles

    • ∠1 and ∠3 are vertically opposite angles.
    • When two lines intersect, vertically opposite angles are equal in measure.

    Complementary Angles

    • The complement of a 40º angle is 50º.
    • If an angle is greater than 45º, its complementary angle is less than 45º.

    Supplementary Angles

    • If two angles are supplementary, their sum is 180 degrees.
    • If two angles are complementary, their sum is 90 degrees.
    • If ∠1 and ∠2 are supplementary and ∠1 is decreased, ∠2 must increase to remain supplementary.

    Parallel Lines and Transversals

    • Alternate interior angles have the same measure.
    • Corresponding angles have the same measure and are in the same relative position.
    • Exterior angles formed by a transversal with parallel lines are supplementary.
    • Alternate exterior angles have the same measure.
    • When drawing a transversal to parallel lines, alternate interior angles are equal in measure.

    Angle Types

    • Adjacent supplementary angles form a linear pair.
    • Vertically opposite angles are equal in measure.
    • Corresponding angles are equal in measure.
    • Alternate interior angles are equal in measure.
    • Alternate exterior angles are equal in measure.

    General Angle Facts

    • When two lines intersect, the vertically opposite angles are equal in measure.
    • The meeting point of two lines when they intersect is called the point of intersection.

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    Test your knowledge on angles with questions about adjacency of angles, finding angle values, filling in blanks about complementary and supplementary angles, and relationships between angles formed by lines intersecting.

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