Angles & Parallel Lines on the ACT

1. In the figure, line m and line n are parallel. The 2 transversals intersect on a point on line m. Which of the following pairs of angles is not necessarily congruent?

• <1 and <2

• <2 and <3

• <2 and <4

• <3 and <4

• <3 and <5

2. In the diagram, lines l and k are cut by transversal r. Lines l and k are NOT parallel. Which of the following MUST be true? They symbol ≅ means 'approximately equal.'

• <1 ≅ <5

• <2 ≅ <8

• <5 ≅ <6

• <5 ≅ <7

• <7 ≅ <3

3. The sum of <B and <C is 90 degrees, and <A ≅ <C. What must be true about the measures of <A and <B?

• m<A + m<B = 90 degrees

• m<A + m<B = 180 degrees

• m<B > m<A

• m<B < m<A

• m<B = m<A

The points X, Y, an Z are collinear. Y is between X and Z, and Q is not on the same line as X, Y, and Z. Which of the following statements about the measure of the angles must be true? (Note: The figure is only 1 possible arrangement of these points.)

• m<XYQ > m<ZYQ

• m<ZYQ > m<XYQ

• The sum of m<XYQ and m<ZYQ is 180°

• The difference of m<XYQ and m<ZYQ is 45°

• The sum of m<XYQ and m<ZYQ is 360°

In the figure, lines a and b are parallel, and line c is a transversal that intersects a and b at D and E. Which of the following must be true?

• y = x

• y = 2x

• x - y = 90°

• x + y = 180°

• x + y = 270°

The figure shows 2 sets of parallel lines: a∥b and c∥d. The acute angle that d intersects a is 65°. What is the measure of the acute angle that c intersects b?

• 15°

• 25°

• 65°

• 75°

• 85°

A metal beam is lifted by a forklift, as shown in the figure. The beam creates and 83 degree angle with the inside of one of the tongs of the forklift. What angle is made between the beam and the other parallel tong?

• 83°

• 87°

• 91°

• 95°

• 97°

In the figure, lines a and b are cut by transversal line c. The 8 angles at the intersections are labeled. When true, which of the following statements cannot always be used to prove that a and b are parallel?

• <1 ≅ <5

• <2 ≅ <6

• <2 ≅ <7

• <3 ≅ <5

• <4 ≅ <5

In the figure below a ∥ b, and transversals c and d intersect a at point X and intersect b at points Y and Z, respectively. Point Q is on b, the measure of <XZQ is 120 degrees, and the measure of <ZXY is 60 degrees. How many of the angles formed by a, b, c, and d have a measure of 60 degrees?

• 4

• 6

• 8

• 10

• 12

In the figure, lines a and b are parallel, line c is transversal, and 3 angle measures are given in degrees. What is the value of m - n?

• -70

• 55

• 70

• 125

• 180