### All High School Math Resources

## Example Questions

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

Solve for . (Not drawn to scale).

**Possible Answers:**

**Correct answer:**

The angles of a triangle must add to 180^{o}. In the triangle to the right, we know one angle and can find another using supplementary angles.

Now we only need to solve for .

### Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

If and , what is the measure of ?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

All of the interior angles of a triangle add up to .

If and , then

Therefore,

Now, will equal because and form a straight line. Therefore,

Also, by definition, the angle of an exterior angle of a triangle is equal to the measure of the two interior angles opposite of it .

### Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Two interior angles in an obtuse triangle measure and . What is the measurement of the third angle.

**Possible Answers:**

**Correct answer:**

Interior angles of a triangle always add up to 180 degrees.

### 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 #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Triangle ABC has angle measures as follows:

What is ?

**Possible Answers:**

57

44

19

79

90

**Correct answer:**

57

The sum of the measures of the angles of a triangle is 180.

Thus we set up the equation

After combining like terms and cancelling, we have

Thus

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

The base angle of an isosceles triangle is five more than twice the vertex angle. What is the base angle?

**Possible Answers:**

**Correct answer:**

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = the vertex angle and = the base angle

So the equation to solve becomes

Thus the vertex angle is 34 and the base angles are 73.

### Example Question #3 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The base angle of an isosceles triangle is 15 less than three times the vertex angle. What is the vertex angle?

**Possible Answers:**

**Correct answer:**

Every triangle contains 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and = base angle

So the equation to solve becomes .

### Example Question #2 : Triangles

The base angle of an isosceles triangle is ten less than twice the vertex angle. What is the vertex angle?

**Possible Answers:**

**Correct answer:**

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = vertex angle and = base angle

So the equation to solve becomes

So the vertex angle is 40 and the base angles is 70

### Example Question #2 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The base angle of an isosceles triangle is 10 more than twice the vertex angle. What is the vertex angle?

**Possible Answers:**

**Correct answer:**

Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.

Let = the vertex angle and = the base angle

So the equation to solve becomes

The vertex angle is 32 degrees and the base angle is 74 degrees

### Example Question #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an isosceles triangle, the vertex angle is 15 less than the base angle. What is the base angle?

**Possible Answers:**

**Correct answer:**

Let = base angle and = vertex angle

So the equation to solve becomes

Thus, 65 is the base angle and 50 is the vertex angle.