Tip #5 to Get a Top ACT Math Score (page 2)
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.
- Vertical angles are equal.
- The angles in a linear pair add up to 180°.
- The angles in a triangle add up to 180°.
If you are given m, then n = 180 – m and m and n are also called supplements, meaning they add up to 180°.
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°.
Correct answer: D
- If the measure of an angle is 42.5°, what is the measure of its supplement?
- Cannot be determined from the given information
- In the figure below, if y = 45 and points A, B, and C lie on the same line, what is the value of z ?
- In the figure below, with angles as marked, if x = 60°, what is the value of y ?
- In the figure below, ABCD is a trapezoid, E lies on , and angle measures are as indicated. If the measure of angle BAD = 49°, what is the measure of ?
- D Honestly this question would usually come with a diagram that makes it easy. But I wanted to make sure that you would learn the term "supplement," which means the angle required to add up to 180°. So the supplement of a 42.5° angle is 180 – 42.5 = 137.5. This question brings up another important issue. As soon as they see "Cannot be determined from the information" as a choice, many students immediately pick it as an answer. There are many urban legends surrounding this. Some say it is always the answer, and others say it is never the answer. Truth: It is sometimes the answer. Specifically, it is sometimes the answer on an "easy" or "medium" question and rarely the answer for a "hard" question.
- K Always mark info from the question into the diagram, so mark y = 45 into the figure. And whenever you see a linear pair, solve the other angle, which in this case equals 180 – 45 = 135. Now we have 4 of the 5 angles of a fivesided figure. Skill #5 tells us that a five-sided figure has 540°, so 540 minus the other angles equals the measure of angle z. z = 540 – 135 – 133 – 139 – 64 = 69.
- E Label the info from the question into the diagram, x = 60. Whenever you see a vertical angle, mark the angle opposite to it. Now, we have two angles of the triangle, 50 and 60. To get the third, subtract these two angles from 180: 180 – 50 – 60 = 70. Now, to get the value of y, which is a linear pair to 70, subtract 70 from 180: 180 – 70 = 110. Careless Error Buster: Remember to finish the question. Don't get 70 and stop. Ask yourself, "Did I finish the question?"
- G Label all info from the question into the diagram. Then fill in the linear pair to CDE: 180 – 110 = 70. Since ABCD is a trapezoid, BC is parallel to AD and angle DCB = 110 (Skill 6 Preview). Now, we have three of the angles of the trapezoid which, since it has four sides, must add up to 360. So 360 – 110 – 49 – 70 = 131. Finally, to get DBA, subtract: 131 – 19 = 112.
Go to: Tip #6
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