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# Tip #6 to Get a Top ACT Math Score (page 2)

By McGraw-Hill Professional
Updated on Sep 7, 2011

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