Tip #7 to Get a Top ACT Math Score

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 (20^th 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

Example Problems

Easy

If triangle MON, shown below, is equilateral, what is the value of x?
1. 30
2. 60
3. 90
4. 120
5. 150

Medium

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?
1. 36°
2. 48°
3. 72°
1. 108°
2. 180°
Hard
In ΔABC, = and the measure of C is 28°. What is the measure of A?
1. 28°
2. 52°
3. 62°
4. 94°
5. 124°
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?
1. 15°
2. 30°
3. 45°
1. 72°
2. 144°