Name the shapes that make up the Texas state flag. Are any of the shapes regular polygons? Explain.
2 answers:
Answer: The answer is Yes.
Step-by-step explanation: The shapes that make up the Texas state flag are rectangle and octagon. Please see attached image.
We can clearly check from the figure that there are three rectangles and one octagon in the flag.
We know that in a rectangle, all the sides are not equal, only the opposite sides are equal, so this figure will not be a regular one.
But, we can check that the octagon in the flag is a regular one because all the eight sides here are equal in measurement.
Thus, there is a shape in the flag which is regular and that is an octagon present in the vertically placed rectangle at the left side of the flag.
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Let
x--------> the measure of the adjacent interior angle
y--------> the measure of an exterior angle at the vertex of a polygon
we know that
The measure of the adjacent interior angle and the measure of an exterior angle at the vertex of a polygon are supplementary angles
so
°
<u>Examples</u>
case 1)
<u>In a square</u>
°
so
°
In this case
The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle
case 2)
<u>an equilateral triangle</u>
°
so
°
In this case
The measure of an exterior angle at the vertex of a polygon is not equals the measure of the adjacent interior angle
therefore
<u>the answer is</u>
sometimes