A regular convex polygon has eight sides. What is the measure of an exterior angle?
2 answers:
<u>Answer:</u>
Exterior angle = 45°
<u>Step-by-step explanation:</u>
We know that the sum of exterior angles of a polygon is 360 degrees.
Since here we a regular polygon with eight sides (which makes it an octagon) so this means that the interior angles each would be equal to:
= 135 degrees
We know that each interior angle is supplementary to the exterior angle at the vertex.
So each exterior angle = = 45 degrees
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Answer:
6. x° is approximately 21.04°
7. x° is approximately 39.56°
8. x° is approximately 58.03°
9. x° is approximately 72.85°
Step-by-step explanation:
6. In the given right triangle (a triangle with the measure of one of the interior angles equal to 90°, indicated by the small square between two sides) , we have;
The hypotenuse side length = 15
The adjacent side to the given reference angle, x° = 14
By trigonometric ratio, we have;
To find the value of x°, we make use of the inverse cosine function, arccos found on a scientific calculator, as follows;
x° = arccos(14/15) ≈ 21.04°
x° ≈ 21.04°
7. In the given right triangle, we have;
The length of the opposite side to the given reference angle, x° = 19
The length of the adjacent side to the given reference angle, x° = 23
By trigonometric ratios, we have;
Therefore;
x° = arctan(19/23) ≈ 39.56°
x° ≈ 39.56°
8. In the given right triangle, the adjacent side to the reference angle, x° and the hypotenuse side are given, therefore, we have;
x° = arccos(9/17) ≈ 58.03°
x° ≈ 58.03°
9. The opposite side to the reference angle and the hypotenuse side are given
By trigonometric ratio, we have;
x° = arcsin(43/45) ≈ 72.85°
x° ≈ 72.85°.