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3 years ago

COMPLETE THIS STATEMENT THE SUM OF THE MEASURES OF THE MEASURES OF THE EXTERIOR ANGLES OF AN N-GON, ONE AT EACH VERTEX IS

Mathematics

1 answer:

ryzh [129]3 years ago

3 0

Answer:

360 degrees

Step-by-step explanation:

we know that

The sum of the n exterior angles for any convex polygon with n sides is always 360 degrees

Example

An equilateral triangle has three equal interior angles measures 60 degrees

Each exterior angle measures 120 degrees

The sum of the exterior angles is equal to 120+120+120=360

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$Use\ the\ quadratic\ formula:\\a^2x+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\if\ \Delta=0\ then\ x_0=\dfrac{-b}{2a}\\\\if\ \Delta < 0\ then\ no\ solution$

$x^2-3x-5=0\\\\a=1;\ b=-3;\ c=-5\\\\\Delta=(-3)^2-4\cdot1\cdot(-5)+3+20=29 \ \textgreater \ 0\\\\\sqrt\Delta=\sqrt{29}\\\\x_1=\dfrac{3-\sqrt{29}}{2\cdot1}=\dfrac{3-\sqrt{29}}{2} \ \textless \ 0\\\\x_2=\dfrac{3+\sqrt{29}}{2\cdot1}=\dfrac{3+\sqrt{29}}{2} \ \textgreater \ 0$

$Answer:\ \boxed{x=\dfrac{3+\sqrt{29}}{2}}$

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