Testinar Grade 8 math

Angle Relationships

Learn to reason about and solve Grade 8 problems involving Angle Relationships.

CH05-09 Geometry and Measurement
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. Two lines intersect. One angle measures 65°. What is \(x\), the measure of an adjacent angle?

    Angle Relationships visual for G8-C05-T09-Q003
    1. 25°
    2. 65°
    3. 115°
    4. 155°

  2. Two lines intersect. One angle is 110°. What is \(a\), the measure of the vertical angle?

    Angle Relationships visual for G8-C05-T09-Q005
    1. 70°
    2. 110°
    3. 140°
    4. 155°

  3. Two parallel lines are cut by a transversal. If the lower angle is 55°, what is \(m\), the alternate interior angle?

    Angle Relationships visual for G8-C05-T09-Q006
    1. 35°
    2. 55°
    3. 125°
    4. 145°

  4. Two parallel lines are cut by a transversal. One angle below the transversal measures 48°. What is \(n\), the corresponding angle above the line?

    Angle Relationships visual for G8-C05-T09-Q008
    1. 42°
    2. 48°
    3. 132°
    4. 138°

  5. Two parallel lines are cut by a transversal. One co-interior (same-side interior) angle is 136°. What is \(y\), the other co-interior angle?

    Angle Relationships visual for G8-C05-T09-Q010
    1. 44°
    2. 136°
    3. 156°
    4. 176°

  6. Two parallel lines are cut by a transversal. The angle marked 62° and angle \(z\) are alternate interior angles. What is \(z\)?

    Angle Relationships visual for G8-C05-T09-Q012
    1. 28°
    2. 62°
    3. 118°
    4. 148°

  7. Two parallel lines are cut by a transversal. One angle measures 78°. What is \(x\), the measure of the corresponding angle on the upper parallel line?

    Angle Relationships visual for G8-C05-T09-Q014
    1. 51°
    2. 78°
    3. 102°
    4. 128°

  8. Two parallel lines are cut by a transversal. The angle \(p\) and the 123° angle are co-interior angles. What is \(p\)?

    Angle Relationships visual for G8-C05-T09-Q016
    1. 57°
    2. 123°
    3. 147°
    4. 180°
Teacher and parent reference

Answer key and explanations

  1. C. 115°

    Adjacent angles on a straight line are supplementary, so they sum to 180°. Thus \(x = 180 - 65 = 115°\).

  2. B. 110°

    Vertical angles are congruent. When two lines intersect, opposite angles are equal, so \(a = 110°\).

  3. B. 55°

    Alternate interior angles are congruent when a transversal cuts parallel lines. So \(m = 55°\).

  4. B. 48°

    Corresponding angles formed by a transversal cutting parallel lines are congruent. So \(n = 48°\).

  5. A. 44°

    Co-interior angles are supplementary when a transversal cuts parallel lines. So \(y = 180 - 136 = 44°\).

  6. B. 62°

    Alternate interior angles formed by a transversal cutting parallel lines are congruent. So \(z = 62°\).

  7. B. 78°

    Corresponding angles are congruent when a transversal cuts parallel lines. So \(x = 78°\).

  8. A. 57°

    Co-interior angles sum to 180°. So \(p = 180 - 123 = 57°\).

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