# ACT Math : How to find an angle in a kite

## Example Questions

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

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

Explanation:

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 : 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.

Not enough information is provided

Explanation:

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 : 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.

Explanation:

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 #1 : How To Find An Angle In A Kite

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

Explanation:

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 #5 : 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.

Explanation:

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 #6 : 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 of the sum of the two remaining interior angles in this kite.

Explanation:

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 #7 : 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.

Explanation:

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 #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 of the sum of the two remaining interior angles.

Explanation:

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 #9 : 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.

Explanation:

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 #10 : How To Find An Angle In A Kite

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

Explanation:

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.

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