Answer:
Exterior Angle = 36 degrees
Step-by-step explanation:
<u><em>Each interior angle of a regular decagon measures 144 degrees.</em></u>
=> <u><em>We'll subtract 144 from 180 to get the measure of the exterior angle.</em></u>
=> Exterior Angle = 180-144
=> Exterior Angle = 36 degrees
Answer:
see explanation
Step-by-step explanation:
Since AB = BC the the triangle is isosceles and thus
∠ A = ∠ C = 8x
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
44x + 8x + 8x = 180, that is
60x = 180 ( divide both sides by 60 )
x = 3
Thus
∠ A = ∠ C = 8x = 8(3) = 24°
∠ B = 44x = 44(3) = 132°
Answer: 37 units
Step-by-step explanation:
This also works as the height of the triangle.
This also works as the base of the triangle.
Let's call pink ''a'', and blue ''b''. The side we're looking for ''c'' is the hypothenuse.
To find the values of a and b, use the area formula of a square and solve for a side. In this case, since we're going to need the squared values, this step can be omitted.
![s=\sqrt[]{A}](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%5D%7BA%7D)
Let's work with Blue.
![s=\sqrt[]{144units^2} \\s=12units](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%5D%7B144units%5E2%7D%20%5C%5Cs%3D12units)
Now Pink.
![s=\sqrt[]{1225units^2}\\s=35units](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%5D%7B1225units%5E2%7D%5C%5Cs%3D35units)
So we have a triangle with a base of 35 units and a height of 12 units.
Now let's use the pythagoream's theorem to solve.
![c^2=a^2+b^2\\c=\sqrt[]{a^2+b^2} \\c=\sqrt[]{(12units)^2+(35units)^2}\\c=\sqrt[]{144units^2+1225units^2}\\ c=\sqrt[]{1369units^2}\\ c=37units](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2%5C%5Cc%3D%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%20%5C%5Cc%3D%5Csqrt%5B%5D%7B%2812units%29%5E2%2B%2835units%29%5E2%7D%5C%5Cc%3D%5Csqrt%5B%5D%7B144units%5E2%2B1225units%5E2%7D%5C%5C%20c%3D%5Csqrt%5B%5D%7B1369units%5E2%7D%5C%5C%20c%3D37units)
