### All High School Math Resources

## Example Questions

### Example Question #3 : Triangles

In the figure above, what is the positive difference, in degrees, between the measures of angle *ACB* and angle *CBD*?

**Possible Answers:**

20

10

40

30

50

**Correct answer:**

10

In the figure above, angle *ADB* is a right angle. Because side *AC* is a straight line, angle *CDB* must also be a right angle.

Let’s examine triangle *ADB*. The sum of the measures of the three angles must be 180 degrees, and we know that angle *ADB* must be 90 degrees, since it is a right angle. We can now set up the following equation.

*x* + *y* + 90 = 180

Subtract 90 from both sides.

*x* + *y* = 90

Next, we will look at triangle *CDB*. We know that angle *CDB* is also 90 degrees, so we will write the following equation:

*y* – 10 + 2*x* – 20 + 90 = 180

*y* + 2*x* + 60 = 180

Subtract 60 from both sides.

*y* + 2*x* = 120

We have a system of equations consisting of *x* + *y* = 90 and *y* + 2*x* = 120. We can solve this system by solving one equation in terms of *x* and then substituting this value into the second equation. Let’s solve for *y* in the equation *x* + *y* = 90.

*x* + *y* = 90

Subtract *x* from both sides.

*y* = 90 – *x*

Next, we can substitute 90 – *x* into the equation *y* + 2*x* = 120.

(90 – *x*) + 2*x* = 120

90 + *x* = 120

*x* = 120 – 90 = 30

*x* = 30

Since *y* = 90 – *x*, *y* = 90 – 30 = 60.

The question ultimately asks us to find the positive difference between the measures of *ACB* and *CBD*. The measure of *ACB* = 2*x* – 20 = 2(30) – 20 = 40 degrees. The measure of *CBD* = *y* – 10 = 60 – 10 = 50 degrees. The positive difference between 50 degrees and 40 degrees is 10.

The answer is 10.

### Example Question #1 : How To Find An Angle In A Right Triangle

If angle and angle , what is the value for angle ?

**Possible Answers:**

**Correct answer:**

For this problem, remember that the sum of the degrees in a triangle is .

That means that .

Plug in our given values to solve:

Subtract from both sides:

### Example Question #4 : Triangles

Which of the following sets of line-segment lengths can form a triangle?

**Possible Answers:**

**Correct answer:**

In any given triangle, the sum of any two sides is greater than the third. The incorrect answers have the sum of two sides equal to the third.

### Example Question #1 : How To Find An Angle In A Right Triangle

In right , and .

What is the value of ?

**Possible Answers:**

48

32

30

24

36

**Correct answer:**

36

There are 180 degrees in every triangle. Since this triangle is a right triangle, one of the angles measures 90 degrees.

Therefore, .