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

\(\displaystyle 180 (n-2)\) degrees, where \(\displaystyle n\) 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: \(\displaystyle 180(4-2)\) degrees \(\displaystyle =180(2)\) degrees \(\displaystyle =360\) 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 \(\displaystyle 360\) degrees and the non-congruent opposite angles sum by \(\displaystyle 2\):   

\(\displaystyle 44+59=103\)

\(\displaystyle 360-103=257\)

This means that \(\displaystyle 257\) is the sum of the remaining two angles, which must be opposite congruent angles. Therefore, the measurement for one of the angles is: 

\(\displaystyle \frac{257}{2}=128.5\) 

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

\(\displaystyle 180 (n-2)\) degrees, where \(\displaystyle n\) 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: \(\displaystyle 180(4-2)\) degrees \(\displaystyle =180(2)\) degrees \(\displaystyle =360\) 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 \(\displaystyle 360\) degrees and the sum of the non-congruent opposite angles.

The solution is:

\(\displaystyle 58+67=125\)

\(\displaystyle 360-125=235$^{\circ}$\)

This means that \(\displaystyle 235$^{\circ}$\) is the sum of the remaining two opposite angles.

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 \(\displaystyle x\) we must first find the values of all of the angles. 

The sum of angles within any quadrilateral is 360 degrees.

Therefore \(\displaystyle \angle D=\angle B\).

To find \(\displaystyle \angle A\):

 \(\displaystyle 360-115-115=130\)

\(\displaystyle 130=2(x+4)=2x+8\)

\(\displaystyle x=\frac{130-8}{2}=\frac{122}{2}=61\)

One of the rules governing kites is that the angles which lie between non-congruent sides are congruent to each other. Thus, we know one of the missing angles is also \(\displaystyle 25^{\circ}\). Since all angles in a quadrilateral must sum to \(\displaystyle 360^{\circ}\), we know that the other missing angle is

\(\displaystyle \angle x = 360^{\circ} - (25^{\circ} + 25^{\circ} + 50^{\circ}) = 260^{\circ}\)

In order to solve this problem, first observe that the red diagonal line divides the kite into two triangles that each have side lengths of \(\displaystyle 15\) and \(\displaystyle 8.\) Notice, the hypotenuse of the interior triangle is the red diagonal. Therefore, use the Pythagorean theorem: \(\displaystyle a^2+b^2=c^2\), where \(\displaystyle c=\) the length of the red diagonal. 

The solution is: 

\(\displaystyle 8^2+15^2=c^2\)

\(\displaystyle 64+225=c^2\)

\(\displaystyle c^2=289\)

\(\displaystyle c=\sqrt{289}=\sqrt{17\times 17}=17\)

To solve this problem, apply the formula for finding the area of a kite: 

\(\displaystyle Area=\frac{diagonalA\times diagonalB}{2}\)

However, in this problem the question only provides information regarding the exact area. The lengths of the diagonals are represented as a ratio, where 
\(\displaystyle diagonalA:diagonalB=1:2\)

Therefore, it is necessary to plug the provided information into the area formula. Diagonal \(\displaystyle A\) is represented by \(\displaystyle x\) and diagonal \(\displaystyle B=2\)\(\displaystyle x\).

The solution is:

\(\displaystyle 196=\frac{x\times 2x}{2}\)

\(\displaystyle 196\times2=x\times 2x\)

\(\displaystyle 392=2x^2\)

\(\displaystyle x^2=\frac{392}{2}=196\)

\(\displaystyle x=\sqrt{196}=14\)

Thus, if \(\displaystyle x=14\), then diagonal \(\displaystyle B\) must equal \(\displaystyle 2(14)=28\)

This problem can be solved by applying the area formula: 



Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal. 

Thus the solution is: 

\(\displaystyle 60=\frac{8\times diagonal B}{2}\)

\(\displaystyle 60\times2=8\times diagonalB\)

\(\displaystyle 120=8(diagonalB)\)

\(\displaystyle diagonal B=\frac{120}{8}=15\)

This problem can be solved by applying the area formula: 



Since this question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal. 

Thus the solution is: 

\(\displaystyle 45=\frac{18\times diagonal B}{2}\)

\(\displaystyle 45\times2=18\times diagonalB\)

\(\displaystyle 90=18(diagonalB)\)

\(\displaystyle diagonal B=\frac{90}{18}=5\)

First find the length of the missing diagonal before you can find the sum of the two perpendicular diagonals. 

To find the missing diagonal, apply the area formula: 




This question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal. 


\(\displaystyle 6,250=\frac{250\times diagonal B}{2}\)

\(\displaystyle 6250\times2=250\times diagonalB\)

\(\displaystyle 12,500=250(diagonalB)\)

\(\displaystyle diagonal B=\frac{12,500}{250}=50\)

Therefore, the sum of the two diagonals is: 

\(\displaystyle 250+50=300\)

You must find the length of the missing diagonal before you can find the sum of the two perpendicular diagonals. 

To find the missing diagonal, apply the area formula: 




This question provides the area of the kite and length of one diagonal, plug that information into the equation to solve for the missing diagonal. 


\(\displaystyle 28=\frac{4\times diagonal B}{2}\)

\(\displaystyle 28\times2=4\times diagonalB\)

\(\displaystyle 56=4(diagonalB)\)

\(\displaystyle diagonal B=\frac{56}{4}=14\)

Therefore, the sum of the two diagonals is: 

\(\displaystyle 14+4=18\)