SAT Math: Lines and Angles

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

Acute Angle

Acute Angle

Less than 90 degrees

Right Angle

Exactly 90 degrees

Obtuse Angle

Greater than 90 degrees but less than 180 degrees

Straight Angle

Exactly 180 degrees

Complementary Angles

Two angles that add up to 90 degrees

Supplementary Angles

Two angles that add up to 180 degrees

Adjacent Angles

Two angles that share a common side and vertex

Vertical Angles

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

Corresponding Angles

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

Alternate Interior Angles

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

Alternate Exterior Angles

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

Consecutive Interior Angles

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

Triangle Angle Sum

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

Angle Sum Theorem

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

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^)

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

• Complement: ( 90^ - 30^ = 60^)

• Supplement: ( 180^ - 30^ = 150^)

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^)

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^)

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^)

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^)