How to find an angle in a kite

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ACT Math › How to find an angle in a kite

Questions 1 - 10

If the diagonals of the quadrilateral above were drawn in the figure, they would form four 90 degree angles at the center. In degrees, what is the value of ?

Explanation

A quadrilateral is considered a kite when one of the following is true:

(1) it has two disjoint pairs of sides are equal in length or

(2) one diagonal is the perpendicular bisector of the other diagonal. Given the information in the question, we know (2) is definitely true.

To find we must first find the values of all of the angles.

The sum of angles within any quadrilateral is 360 degrees.

Therefore $\angle D=\angle B$ .

To find $\angle A$ :

$x=\frac{130-8}{2}=\frac{122}{2}=61$

Kite vt act

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

$295$^{\circ}$$

$147.5$^{\circ}$$

$75$^{\circ}$$

$300$^{\circ}$$

$300.5$^{\circ}$$

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:

A kite has one set of opposite interior angles where the two angles measure $28$^{\circ}$$ and $84$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

$124$^{\circ}$$

$248$^{\circ}$$

$112$^{\circ}$$

$84^2$^{\circ}$$

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.

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:

$\frac{248}{2}=124$

A kite has one set of opposite interior angles where the two angles measure $118$^{\circ}$$ and $51$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

$95.5$^{\circ}$$

$95$^{\circ}$$

$191$^{\circ}$$

$169$^{\circ}$$

$59.5$^{\circ}$$

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:

$\frac{191}{2}=95.5$

A kite has one set of opposite interior angles where the two angles measure $91$^{\circ}$$ and $99$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

$85$^{\circ}$$

$170$^{\circ}$$

$190$^{\circ}$$

$95$^{\circ}$$

$72$^{\circ}$$

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.

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:

$\frac{170}{2}=85$

A kite has one set of opposite interior angles where the two angles measure $82$^{\circ}$$ and $58$^{\circ}$$ , respectively. Find the measurement of the sum of the two remaining interior angles in this kite.

$220$^{\circ}$$

$110$^{\circ}$$

$105$^{\circ}$$

$140$^{\circ}$$

$240$^{\circ}$$

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.

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:

A kite has one set of opposite interior angles where the two angles measure $16$^{\circ}$$ and $187$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

$78.5$^{\circ}$$

$87.5$^{\circ}$$

$157$^{\circ}$$

$203$^{\circ}$$

$204.5$^{\circ}$$

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.

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:

$\frac{157}{2}=78.5$

Kite vt act

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

$175$^{\circ}$$

$87.5$^{\circ}$$

$187.5$^{\circ}$$

$264$^{\circ}$$

$106$^{\circ}$$

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.

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.

A kite has one set of opposite interior angles where the two angles measure $44$^{\circ}$$ and $59$^{\circ}$$ , respectively. Find the measurement for one of the two remaining interior angles in this kite.

$128.5$^{\circ}$$

$103$^{\circ}$$

$257$^{\circ}$$

$65.5$^{\circ}$$

$130.5$^{\circ}$$

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.

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:

$\frac{257}{2}=128.5$

A kite has one set of opposite interior angles where the two angles measure $58$^{\circ}$$ and $67$^{\circ}$$ , respectively. Find the measurement of the sum of the two remaining interior angles.