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# Tip #6 to Get a Top ACT Math Score

By McGraw-Hill Professional
Updated on Sep 7, 2011

Most ACTs have one question involving parallel lines. In math class, learning about parallel lines might have seemed pretty tricky—alternate interior angles, corresponding angles, same-side interior angles. … We don't need all that vocab for the ACT. We just need to know:

• Parallel lines are two lines that never touch.
• If two parallel lines are crossed by another line (called a transversal), then eight angles form.
• These eight angles are of two types, big or little. All bigs are equal, and all littles are equal.

This is enough to answer any parallel-lines ACT question.

There's another point!

Let's look at this question:

Solution: This question may look tough at first, but it uses Skill 6 exactly, and we're ready for it. In the pair of parallel lines crossed by segment NM, several angles are formed, and ONM is a smaller-looking angle and is congruent (congruent is just a fancy geometry word for "equal") to all other smaller-looking angles of the angles formed. XMN is another smaller-looking angle, so ONM = XMN. YNM and ZMN are bigger-looking angles and are equal to each other, but not to ONM.

### Easy

1. In the figure below, m || n. If y = 37.5°, what is the value of x ?
1. 42.5
2. 100
3. 137.5
4. 142.5
5. 180
2. If x = 73° and p || q and m || n in the four lines shown, what is the value of z?
1. 17
2. 73
3. 90
1. 97
2. 107

### Medium

3. In the figure below, m || n. If z = 42.5 and x = 125, then y =?
1. 97.5
2. 87.5
3. 57.5
4. 47.5
5. 27.5
4. If z = 55° and y = 75° in the picture below, then which of the following must be true?
1. p || q
2. x + y = 180°
3. z = x
1. x + z = 180°
2. y = 2x

### Hard

5. In the figure below, V, W, X, and Y are collinear; Z, W, and T are collinear; and the angles at V, X, and T are right angles, as marked. Which of the following statements is NOT justifiable from the given information?
1. is perpendicular to
2. VZW is congruent to XTW.
3. is congruent to
4. ΔZVW is similar to ΔTXW.
5. is parallel to

1. D   In a pair of parallel lines there are only two kinds of angles, big and little, and the two add up to 180. Here y is a little angle and x is clearly a bigger angle, so they add up to 180, and x = 180 – 37.5 = 142.5.
2. K   Parallel lines cut by a transversal make 2 kinds of angles, big and little. Clearly x is little and z is big. If x = 73, then z = 180 – 73 = 107.
3. A   First, mark the info that is given in the question into the diagram. That always helps to make the question simpler and usually shows which strategies to use. Then use vertical angles, linear pairs, and triangles to calculate the measures of any other angles that you can. The vertical angle to z is 42.5, and the linear pair to x is 55, so now we have two angles of the triangle. 180 – 42.5 – 55 = 82.5. And the linear pair of 82.5, which is y, is 180 – 82.5 = 97.5 = y.
4. G   Mark the info from the question into the diagram. Then mark all other angles that you can determine. Here x and y are a linear pair, so x + y = 180 and x = 180 – 75 = 105. Since z, x, and y are three different numbers, they cannot be the angles of two parallel lines, which are always at most two different numbers. Also, since x and z are both less than 90, lines p and q cannot be parallel—they are heading toward each other and will intersect. Only G is the true choice.
5. C   Only choice C is NOT justifiable:
1. is perpendicular to —justifiable as marked
2. VZW is congruent to —justifiable, all small angles are equal in the pair of parallel lines
3. is congruent to —NOT justifiable, we have no proof
4. ΔZVW is similar to ΔTXW—(Skill 26 Preview) yes, the angles of ΔZVW are equal to the corresponding angles of ΔTXW, and therefore the triangles are similar
5. is parallel to —justifiable, both are perpendicular to and therefore parallel to each other

Go to: Tip #7