### All SAT II Math II Resources

## Example Questions

### Example Question #1 : Finding Angles

**Possible Answers:**

**Correct answer:**

The angles containing the variable all reside along one line, therefore, their sum must be .

Because and are opposite angles, they must be equal.

### Example Question #1 : Finding Angles

What angle do the minute and hour hands of a clock form at 6:15?

**Possible Answers:**

**Correct answer:**

There are twelve numbers on a clock; from one to the next, a hand rotates . At 6:15, the minute hand is exactly on the "3" - that is, on the position. The hour hand is one-fourth of the way from the "6" to the "7" - that is, on the position. Therefore, the difference is the angle they make:

.

### Example Question #2 : Finding Angles

In triangle , and . Which of the following describes the triangle?

**Possible Answers:**

is acute and scalene.

is acute and isosceles.

is obtuse and scalene.

None of the other responses is correct.

is obtuse and isosceles.

**Correct answer:**

is acute and isosceles.

Since the measures of the three interior angles of a triangle must total ,

All three angles have measure less than , making the triangle acute. Also, by the Isosceles Triangle Theorem, since , ; the triangle has two congruent sides and is isosceles.

### Example Question #3 : Finding Angles

In , and are complementary, and . Which of the following is true of ?

**Possible Answers:**

is right and scalene.

is acute and scalene.

is right and isosceles.

None of the other responses is correct.

is acute and isosceles.

**Correct answer:**

is right and scalene.

and are complementary, so, by definition, .

Since the measures of the three interior angles of a triangle must total ,

is a right angle, so is a right triangle.

and must be acute, so neither is congruent to ; also, and are not congruent to each other. Therefore, all three angles have different measure. Consequently, all three sides have different measure, and is scalene.

### Example Question #1 : Finding Angles

The above figure is a regular decagon. Evaluate .

**Possible Answers:**

**Correct answer:**

As an interior angle of a regular decagon, measures

.

Since and are two sides of a regular polygon, they are congruent. Therefore, by the Isosceles Triangle Theorem,

The sum of the measures of a triangle is , so

### Example Question #5 : Finding Angles

The above hexagon is regular. What is ?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

Two of the angles of the quadrilateral formed are angles of a regular hexagon, so each measures

.

The four angles of the quadrilateral are . Their sum is , so we can set up, and solve for in, the equation:

### Example Question #6 : Finding Angles

What angle do the minute and hour hands of a clock form at 4:15?

**Possible Answers:**

**Correct answer:**

There are twelve numbers on a clock; from one to the next, a hand rotates . At 4:15, the minute hand is exactly on the "3" - that is, on the position. The hour hand is one-fourth of the way from the "4" to the "5" - that is, on the position. Therefore, the difference is the angle they make:

.

### Example Question #7 : Finding Angles

If the vertical angles of intersecting lines are: and , what must be the value of ?

**Possible Answers:**

**Correct answer:**

Vertical angles of intersecting lines are always equal.

Set the two expressions equal to each other and solve for .

Subtract from both sides.

Subtract 6 from both sides.

The answer is:

### Example Question #1 : Finding Angles

If the angles in degrees are and which are complementary to each other, what is three times the value of the smallest angle?

**Possible Answers:**

**Correct answer:**

Complementary angles add up to 90 degrees.

Set up an equation such that the sum of both angles equal to 90.

Subtract 10 from both sides.

Divide by 2 on both sides.

The angles are:

Three times the value of the smallest angle is:

The answer is:

### Example Question #9 : Finding Angles

If the angles and are supplementary, what must be the value of ?

**Possible Answers:**

**Correct answer:**

Supplementary angles sum up to 180 degrees.

Add five on both sides.

Divide by negative five on both sides to determine .

The answer is:

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