A study of sleep patterns randomly selected participants in the study to sleep in either a dark room or a room with light.
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<u>Given</u>:
Given that the measure of arc DF is 162°
We need to determine the measure of ∠E
<u>Measure of ∠E:</u>
The measure of ∠E can be determined using the inscribed angle theorem.
Thus, by inscribed angle theorem, we have;
Substituting , we get;
Dividing, we get;
Thus, the measure of ∠E is 81°
The length of the diagonal of the rectangle will be 14.142 units.
<h3>What exactly is a rectangle?</h3>
It has four sides and is a polygon. The internal angle total is 360 degrees. The opposing sides of a rectangle are parallel and equal, and each angle is 90 degrees.
Rectangle diagonals are equally equal and meet at the midpoint.
O is the circle's center, MNOP is its rectangle, and the circle's area is 100 in the diagram to the left.
Area of circle=πr²
100 π= πr²
r= 10 units
The length of the rectangle is equal to the radius of the circle is 10 units. The length of the diagonal is √2 times the side of the rectangle;
L=√2 R
L=1.414×10
L=14.14
Hence the length of the diagonal of the rectangle will be 14.142 units.
To learn more about the rectangle, refer to the link brainly.com/question/13747846.
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