ACT Math : How to find an angle in a kite

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

Kite vt act

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

Possible Answers:

Correct answer:

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 #1 : 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:

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 #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. 

Possible Answers:

Correct answer:

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 #2 : Kites

Kite vt act

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

Possible Answers:

Correct answer:

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 #4 : 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:

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

Possible Answers:

Correct answer:

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 #4 : 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:

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 #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:

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 #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 for one of the two remaining interior angles in this kite. 

Possible Answers:

Correct answer:

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 #4 : Kites

Kite vt act

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

Possible Answers:

Correct answer:

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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