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# Tip #5 to Get a Top ACT Math Score

By Brian Leaf
McGraw-Hill Professional
Updated on Sep 7, 2011

Every ACT has two or three geometry questions that ask you to find the measure of an angle. Many students panic, "I don't remember the million postulates we learned." Good news, you only need a small handful of those million postulates to solve most geometry questions.

Skills 5 to 7 teach you everything that you need to find the measure of an angle on the ACT; memorize these skills and you will gain points, guaranteed.

1. Vertical angles are equal.
2. The angles in a linear pair add up to 180°.
3. If you are given m, then n = 180 – m and m and n are also called supplements, meaning they add up to 180°.

4. The angles in a triangle add up to 180°.
5. The angles in a 4-sided shape add up to 360°.

The angles in a 5-sided shape add up to 540°.

The angles in a 6-sided shape add up to 720°.

Let's look at this question:

Solution: First, always mark all info from the question into the diagram. This helps you see what to do next. This question uses two of our strategies: linear pair and 360° in a four-sided shape. Whenever you are given the measure of one angle in a linear pair of angles, determine the measure of the other angle in the pair. This always brings you toward the right answer; it's what the ACT wants you to do. So the angle next to the 140° must be 180 – 140 = 40°. Now, we have three of four angles which must add up to 360°, so the fourth must be 360 – 100 – 40 – 77 = 143°.

### Easy

1. If the measure of an angle is 42.5°, what is the measure of its supplement?
1. 47.5°
2. 57.5°
3. 132.5°
4. 137.5°
5. Cannot be determined from the given information
2. In the figure below, if y = 45 and points A, B, and C lie on the same line, what is the value of z ?

1. 204
2. 135
3. 84
1. 72
2. 69

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