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Mathematics 8 Online
princeevee:

i need some help please with geometry

princeevee:

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princeevee:

@Hero

princeevee:

@Vocaloid

princeevee:

@Pixel

Pixel:

its a quadrilateral so the measure of allangles is 360

princeevee:

so since we have one of the angles, do we subtract 82 from 360?

Vocaloid:

|dw:1555096274102:dw| opposite angles are supplementary <A + <C = 180 you have <C so just solve for <A

princeevee:

98?

Vocaloid:

perfect

princeevee:

think you can help with some more?

Vocaloid:

maybe, I'll do what I can before I have to go

princeevee:

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princeevee:

so what i see here now with the knowledge i've gained from the last question, i first find X, then i subtract whatever 2x+4 is by 180?

Vocaloid:

you're on the right track you can start with <B + <D = 180 to solve for x then plug into <A then solve <A + <C = 180 for <C

princeevee:

x= 48

Vocaloid:

good, keep going

princeevee:

which makes <a 100, meaning angle c is 80

Vocaloid:

perfect, 80 = your sol'n

princeevee:

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Vocaloid:

hm I got something diff. I think s = r * theta (as long as we're in radians) where s is the arc length, r is radius, theta is the angle

Vocaloid:

plugging in the numbers 7.2 = 8 * theta

princeevee:

so the answer is 8?

Vocaloid:

you need to solve for theta

princeevee:

now i'm slightly getting confused now

Vocaloid:

the formula for arc length in terms of theta (the central angle of a circle), r (the radius), and s (the arc length) is s = r * theta you are given s = 7.2 cm, and r = 8, so plug these into the equation and solve for theta. theta is your solution.

Vocaloid:

|dw:1555097447312:dw|

princeevee:

theta would have to be a negative, right?

Vocaloid:

? no, both sides of the equation are positive so theta must be positive

Vocaloid:

7.2 = 8 * theta you just need to divide both sides by 8 to isolate theta

princeevee:

0.9?

Vocaloid:

good, theta = 0.9 radians

princeevee:

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Vocaloid:

hm I got something a lot larger s = r * theta r = 36.9, theta = 8*3.14/5, solve for s

princeevee:

25.12 was what 8pi/5 was,

Vocaloid:

8 * 3.14 / 5 = 5.024 (which was your original answer) but keep in mind you also need to multiply by the radius (36.9) so 5.024 * (36.9) = ?

princeevee:

185.38

Vocaloid:

almost 185.3856 is the full solution which rounds to 185.39

Vocaloid:

i have time for like one more before I gotta start driving home

princeevee:

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Vocaloid:

ok, this is area of a sector which is a bit different than arc length (theta/2pi) * pi * r^2 where theta is the central angle and r is the radius

Vocaloid:

ok I actually need to go now but (5 * 3.14 / 6) / (2 * 3.14) * 3.14 * (5.6)^2 with everything plugged in

princeevee:

41.03

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