SAT Math: Lines and Angles

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These flashcards are ONLY information for the lines & angles section of the SAT's. Ultimately, background knowledge that can help you with difficult questions

SAT

Math

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21 Terms

1
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Acute Angle

Less than 90 degrees

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Right Angle

Exactly 90 degrees

3
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Obtuse Angle

Greater than 90 degrees but less than 180 degrees

4
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Straight Angle

Exactly 180 degrees

5
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Complementary Angles

Two angles that add up to 90 degrees

6
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Supplementary Angles

Two angles that add up to 180 degrees

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Adjacent Angles

Two angles that share a common side and vertex

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Vertical Angles

Opposite angles formed by two intersecting lines; they are always equal

9
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Corresponding Angles

Angles in the same relative position at each intersection; they are equal

10
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Alternate Interior Angles

Angles on opposite sides of the transversal but inside the parallel lines; they are equal

11
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Alternate Exterior Angles

Angles on opposite sides of the transversal but outside the parallel lines; they are equal

12
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Consecutive Interior Angles

Angles on the same side of the transversal and inside the parallel lines; they add up to 180 degrees

13
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Triangle Angle Sum

The sum of the interior angles of a triangle is always 180 degrees.

14
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Angle Sum Theorem

The sum of the interior angles of a triangle is 180 degrees: ( angle A + angle B + angle C = 180).

15
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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.

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Parallel Lines and Transversals

  • Corresponding angles are equal: ( angle 1 = angle 5 )

  • Alternate interior angles are equal: ( angle 3 = angle 6 )

  • Alternate exterior angles are equal: ( angle 2 = angle 7 )

  • Consecutive interior angles are supplementary: ( angle 4 + angle 6 = 180^)

17
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If ( angle A = 30^), find its complement and supplement.

  • Complement: ( 90^ - 30^ = 60^)

  • Supplement: ( 180^ - 30^ = 150^)

18
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If two intersecting lines form angles such that one angle is 40^, find the measures of all angles.

  • Vertical angles: ( 40^) and ( 40^)

  • Adjacent angles: ( 140^) and ( 140^)

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If two parallel lines are cut by a transversal and one of the alternate interior angles is 85^, find all the other angles.

  • Alternate interior angle: ( 85^)

  • Corresponding angle: ( 85^)

  • Consecutive interior angle: ( 180^- 85^= 95^)

  • Alternate exterior angle: ( 85^)

20
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In triangle ABC, if ( angle A = 50^) and ( angle B = 60^), find ( angle C ).

  • ( angle C = 180^ - angle A - angle B )

  • ( angle C = 180^ - 50^- 60^ = 70^)

21
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In triangle DEF, if the exterior angle at vertex E is ( 120^) and the interior opposite angles are ( angle D = 70^) and ( angle F = x ), find ( x ).

  • ( 120^ = 70^ + x )

  • ( x = 120^ - 70^= 50^)