Answer:
Step-by-step explanation:
Given a circle centre J
Let the radius of the circle =r
LK is tangent to circle J at point K
From the diagram attached
Theorem: The angle between a tangent and a radius is 90 degrees.
By the theorem above, Triangle JLK forms a right triangle with LJ as the hypotenuse.
Using Pythagoras Theorem:
The length of the radius,
The measures of the missing angles in the kite are given as follows:
The sum of the internal angle measures of a polygon of n sides is given by the equation presented as follows:
S = (n - 2) x 180º.
The kite, as shown by the image at the end of the answer, has 4 sides, hence the sum of the measures is given as follows:
S = (4 - 2) x 180º
S = 2 x 180º
S = 360º.
Angles B and D are on the opposite side of the kite, as shown by the image at the end of the answer, hence they are congruent and:
B = 109º.
Adding the measures, the value of x is obtained as follows:
5x + 14 + 109 + 3x + 8 + 109 = 360
8x = 164
x = 20.5.
Hence the measures are given as follows:
The model of the kite, with different angle measures, is given by the image at the end of the answer.
More can be learned about the internal angles of a polygon at brainly.com/question/224658
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