The measure of the angles are [tex]\angle A=36.87^{\circ}[/tex], [tex]\angle B=36.87^{\circ}[/tex], [tex]\angle C=143.13^{\circ}[/tex] and [tex]\angle D=143.13^{\circ}[/tex]
Explanation:
The height of an isosceles trapezoid is 6.
The bases are 4 and 20.
The image of the trapezoid showing these measurements is attached below:
Thus, DC = 4 and AB = 20.
Using pythagorean theorem,
AB = [tex]\sqrt{8^2+6^2} =\sqrt{64+36} =10[/tex]
Thus, AB = 10
Now, we shall determine the angles [tex]\angle A, \angle B, \angle C[/tex] and [tex]\angle D[/tex]
[tex]\sin \angle A=\frac{6}{10}[/tex]
[tex]\angle A=sin^{-1}(\frac{6}{10})[/tex]
[tex]\angle A=36.87^{\circ}[/tex]
To determine [tex]\angle D[/tex], let us add [tex]\angle A[/tex] and [tex]\angle D[/tex] and equating it to 180°
[tex]\angle A+ \angle D=180[/tex]
[tex]36.87+\angle D=180[/tex]
[tex]\angle D=143.13^{\circ}[/tex]
Since, [tex]\angle A=\angle B[/tex] and [tex]\angle D=\angle C[/tex] , we have,
[tex]\angle B=36.87^{\circ}[/tex] and [tex]\angle C=143.13^{\circ}[/tex]
Thus, the measures of the angles of the trapezoid are [tex]\angle A=36.87^{\circ}[/tex], [tex]\angle B=36.87^{\circ}[/tex], [tex]\angle C=143.13^{\circ}[/tex] and [tex]\angle D=143.13^{\circ}[/tex]
