### All ACT Math Resources

## Example Questions

### Example Question #1 : Kites

Using the kite shown above, find the sum of the two remaining congruent interior angles.

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

To find the sum of the remaining two angles, determine the difference between degrees and the sum of the non-congruent opposite angles.

The solution is:

degrees

Thus, degrees is the sum of the remaining two opposite angles.

Check:

### Example Question #2 : Kites

A kite has one set of opposite interior angles where the two angles measure and , respectively. Find the measurement for one of the two remaining interior angles in this kite.

**Possible Answers:**

Not enough information is provided

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between degrees and the non-congruent opposite angles sum by :

This means that is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

### Example Question #3 : Kites

A kite has one set of opposite interior angles where the two angles measure and , respectively. Find the measurement for one of the two remaining interior angles in this kite.

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

A kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between degrees and the non-congruent opposite angles sum by :

This means that is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

### Example Question #3 : Kites

Using the kite shown above, find the sum of the two remaining congruent interior angles.

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

A kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

To find the sum of the remaining two angles, determine the difference between degrees and the sum of the non-congruent opposite angles.

The solution is:

degrees

Thus, degrees is the sum of the remaining two opposite angles.

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

A kite has one set of opposite interior angles where the two angles measure and , respectively. Find the measurement for one of the two remaining interior angles in this kite.

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between degrees and the non-congruent opposite angles sum by :

This means that is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

### Example Question #5 : Kites

A kite has one set of opposite interior angles where the two angles measure and , respectively. Find the measurement of the sum of the two remaining interior angles in this kite.

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

To find the sum of the remaining two angles, determine the difference between degrees and the sum of the non-congruent opposite angles.

The solution is:

degrees

This means that degrees is the sum of the remaining two opposite angles and that each have an individual measurement of degrees.

Check:

### Example Question #2 : How To Find An Angle In A Kite

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

A kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between degrees and the non-congruent opposite angles sum by :

This means that is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

### Example Question #3 : Kites

A kite has one set of opposite interior angles where the two angles measure and , respectively. Find the measurement of the sum of the two remaining interior angles.

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

To find the sum of the remaining two angles, determine the difference between degrees and the sum of the non-congruent opposite angles.

The solution is:

degrees

This means that degrees is the sum of the remaining two opposite angles.

Check:

### Example Question #8 : Quadrilaterals

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

The missing angle can be found by finding the sum of the non-congruent opposite angles. Then divide the difference between degrees and the non-congruent opposite angles sum by :

This means that is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is:

### Example Question #8 : How To Find An Angle In A Kite

Using the kite shown above, find the sum of the two remaining congruent interior angles.

**Possible Answers:**

**Correct answer:**

The sum of the interior angles of any polygon can be found by applying the formula:

degrees, where is the number of sides in the polygon.

A kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & **one set of congruent opposite angles**.

To find the sum of the remaining two angles, determine the difference between degrees and the sum of the non-congruent opposite angles.

The solution is:

degrees

degrees

Thus, degrees is the sum of the remaining two opposite angles.