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Test PrepACTMathLines & Angles

ACT Math Skill Review: Lines & Angles

The ACT Math test contains a fair number of questions that will test your knowledge of Geometry. Indeed, 45% of the test is focused on geometry and trigonometry. In particular, one area that will be tested is the relationship between points, lines and angles and the figures they form.

Definitions

  • A line extends forever in either direction. The line below, called l, has three points on it: A, B, and C. The part of the line between points is called a line segment. For example, the line segment between points A and B will be referred to as either “segment AB” or simply AB. Points A and B are the endpoints of segment AB.
LinesGraph.PNG
  • Angles are most often described by the points on the lines that intersect to form the angle or by the point of intersection itself. For instance, in the diagram below, angle ABC could be described as either ∠ABC or ∠x.LinesAndAngles2.PNG
  • A line forms an angle of 180°. If that line is cut by another line, it divides the 180° into two pieces that together add up to 180°. In the example above, ∠x + ∠y = 180°. As a result, they are called supplementary angles. Any two angles that add up to 180° are supplementary angles.
         LinesAndAngles3-(1).PNG
  • When two lines intersect, they form four angles, represented above by the letters A, B, C, and D. ∠A and ∠B together form a straight line, so they add up to 180°. The same is true for ∠C and ∠D, ∠A and ∠D, or ∠B and ∠C. Since there are 180° above the line (∠A + ∠B), there are also 180° below the line (∠C + ∠D). Therefore, the sum of the four angles is 360°. ∠A and ∠C are opposite from each other and always equal to each other, as are ∠B and ∠D. These are known as vertical angles.
        LinesAndAngles4.PNG
  • When two lines meet so that 90° angles are formed, the lines are said to be perpendicular to each other. The 90° angle is called a right angle. A right angle is represented by a little box at the point of intersection of the two lines. The perpendicularity of lines l1 and l2 in the figure above is represented as l1l2.
        LinesAndAngles5.PNG
  • Two angles whose sum is 90°, or one right angle, are said to be complementary. For instance, in the figure above, ∠AOB is the complement of ∠BOC. Thus, ∠AOB + ∠ BOC = 90°.
    LinesAndAngles6.PNG
  • Two lines in the same plane that are equally distant from one another at all points are called parallel lines. Parallel lines never meet. Parallel lines are often represented as l1||l2.
        LinesAndAngles7.PNG
  • When parallel lines are cut by a third line (known as a transversal), eight angles are formed(∠A,∠B,∠C,∠D,∠E,∠F,∠G, and ∠H). Based on what you've learned about parallel lines, ∠A = ∠C and ∠B = ∠D. Since the same transversal cuts đť‘™2, the four angles ∠E, ∠F, ∠G, and ∠H are in the same proportions as the angles above. Thus, ∠E = ∠A and ∠F = ∠B.

Example

Let's try a problem, applying what we learned above.
LinesAndAngles8.PNG

  1. If l1 || l2, what is the value of x + y?

    1. 50°
    2. 60°
    3. 130°
    4. 180°
    5. 360°

Answer and Explanation

  1. The correct answer is D. The question stem tells us that the two lines are parallel. Thus, we know that x is equal to 130°. Since 130° and y° form a straight line, we know that they must total 180°. Thus, x + y = 180°.  


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