Tip #7 to Get a Top ACT Math Score (page 2)
Sir Bedevere:… And that, my liege, is how we know the Earth to be banana-shaped. King Arthur: This new learning amazes me, Sir Bedevere. Explain again how sheeps' bladders may be employed to prevent earthquakes.
Monty Python and the Holy Grail (20th Century Fox, 1975)
By the end of this Skill, you will have learned all that you need to know about angles for the ACT. That's great news because every ACT includes several angle questions, and now you can always get them right. You know what to expect, you know what to use, and you will earn more points!
Back in geometry class, you had a full chapter with 14 theorems classifying triangles. Here are two that matter for the ACT.
- If a triangle is isosceles (a fancy term for having two equal sides), then the two angles opposite the equal sides are also equal.
- If a triangle is equilateral (a fancy term for having all sides equal), then it has all equal angles of 60° each.
Let's take a look at this question:
Solution: As soon as you are given info in the question, mark it in the diagram. This will remind you which geometry Skill to use: since two sides are equal in the triangle, the two angles opposite the two sides are also equal. So b = c. Therefore, b ≠ c definitely CANNOT be true. All other answers are possible since segment NO might also equal segments MN and MO.
Correct answer: B
- If triangle MON, shown below, is equilateral, what is the value of x?
- In the figure below, is parallel to with A on and S on . Also PS = SQ, and the measure of APS is 108°. What is the measure of PSQ?
- In ΔABC, = and the measure of C is 28°. What is the measure of A?
- If the area of a right triangle is 72, and the measure of one leg is 12, which of the following could be the value of one of its angles?
- D As soon as you see an equilateral triangle, mark each angle 60°. Then since x forms a linear pair with 60° angle , x = 180 – 60 = 120.
- F When you are given one angle in a linear pair, mark the other. So = 180 – 108 = 72. And as soon as you see two sides of a triangle are equal, mark their opposite angles equal. So since PS = SQ, = . We already determined that = 72, so must also equal 72. Then since the angles in a triangle must add up to 180, = 180 – 72 – 72 = 36.
- E When a picture is described, but not shown, draw it. Then, this "hard" question is cake for us. We know to draw a diagram, and we know what to do when we see an isosceles triangle.
- H This question is rated "hard," but easy with our Skills!
Since AB - AC, we know that base angles and are equal, and therefore angle B also equals 28. Then since the three angles of the triangle must add up to 180, angle A = 180 – 28 – 28 = 124.
Area = 0.5(base)(height)
72 = 0.5(12)(x)
So x = 12 and the triangle is isosceles, which we know means that the base angles are equal. Since it's a right triangle, the base angles must add up to 90, since 180 – the right angle = 90 to be shared by the base angles. Since they are equal, they are 90/2 = 45° each.
Go to: Tip #8
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