### All HSPT Math Resources

## Example Questions

### Example Question #1 : How To Find The Measure Of An Angle

What is the sum of the interior angles of a triangle?

**Possible Answers:**

**Correct answer:**

The sum of the three interior angles of a triangle is degrees.

### Example Question #2 : How To Find The Measure Of An Angle

Two of the interior angles of a triangle measure and . What is the greatest measure of any of its exterior angles?

**Possible Answers:**

It cannot be determined from the information given.

**Correct answer:**

The interior angles of a triangle must have measures whose sum is , so the measure of the third angle must be .

By the Triangle Exterior-Angle Theorem, an exterior angle of a triangle measures the sum of its remote interior angles; therefore, to get the greatest measure of any exterior angle, we add the two greatest interior angle measures:

### Example Question #1 : Geometry

Two angles are supplementary and have a ratio of 1:4. What is the size of the smaller angle?

**Possible Answers:**

**Correct answer:**

Since the angles are supplementary, their sum is 180 degrees. Because they are in a ratio of 1:4, the following expression could be written:

### Example Question #1 : Acute / Obtuse Triangles

In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?

**Possible Answers:**

**Correct answer:**

Since the sum of the angles of a triangle is , and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

### Example Question #58 : Geometry

The measure of 3 angles in a triangle are in a 1:2:3 ratio. What is the measure of the middle angle?

**Possible Answers:**

**Correct answer:**60

The angles in a triangle sum to 180 degrees. This makes the middle angle 60 degrees.

### Example Question #1 : How To Find The Measure Of An Angle

Call the three angles of a triangle .

The measure of is twenty degrees greater than that of ; the measure of is thirty degrees less than twice that of . If is the measure of , then which of the following equations would we need to solve in order to calculate the measures of the angles?

**Possible Answers:**

**Correct answer:**

The measure of is twenty degrees greater than the measure of , so its measure is 20* added to* that of - that is, .

The measure of is thirty degrees less than twice that of . Twice the measure of is , and thirty degrees less than this is 30 *subtracted from* - that is, .

The sum of the measures of the three angles of a triangle is 180, so, to solve for - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

### Example Question #4 : How To Find The Measure Of An Angle

Call the three angles of a triangle .

The measure of is forty degrees less than that of ; the measure of is ten degrees less than twice that of . If is the measure of , then which of the following equations would we need to solve in order to calculate the measures of the angles?

**Possible Answers:**

**Correct answer:**

The measure of is forty degrees less than the measure of , so its measure is 40* subtracted from* that of - that is, .

The measure of is ten degrees less than twice that of . Twice the measure of is , and ten degrees less than this is 10* subtracted from* - that is, .

The sum of the measures of the three angles of a triangle is 180, so, to solve for - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

### Example Question #5 : How To Find The Measure Of An Angle

Two interior angles of a triangle adds up to degrees. What is the measure of the other angle?

**Possible Answers:**

**Correct answer:**

The sum of the three angles of a triangle add up to 180 degrees. Subtract 64 degrees to determine the third angle.

### Example Question #6 : How To Find The Measure Of An Angle

What is of the measure of a right angle?

**Possible Answers:**

**Correct answer:**

A right angle has a measure of . One fifth of the angle is:

### Example Question #7 : How To Find The Measure Of An Angle

What angle is complementary to ?

**Possible Answers:**

**Correct answer:**

To find the other angle, subtract the given angle from since complementary angles add up to .

The complementary is: