Help me with geometry hw?

1) in an equilateral triangle, the interior angles are all 60º

the exterior angle is always 120º

120 - 60 = 60, do this for every all three angle 3 * 60 = 180º

answer A

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2) use the pythagorean theorem

(2√5)^2 + 5^2 = c^2

20 + 25 = c^2

45 = c^2

√45 = c

could a mistake have occurred when the answers were typed in?

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3) complementary angle add up to 90º

5x + x = 90

6x = 90º

x = 15º

the larger angle is 5x = 5 * 15 = 75º

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4) Use the pythagorean theorem again

10^2 + 4^2 = c^2

100 + 16 = c^2

√116 = c

√(4 * 29) = c

2√29 = c

(1) Just to be awkward, I maintain that none of the answers is correct. Draw an equilateral triangle (a rough sketch wil do). Now extend all three sides in both directions; the angles of an equilateral triangle are each 60 degrees, with a total of 180 degrees; now if you look at the diagram, you will see that you have three angles of 60 degrees outside the triangle (each vertically opposite an angle of 60 degrees inside the triangle); at each vertex of the triangle, where you have extended a side, the side makes an angle of 120 degrees with an extended side, and there are 6 angles like that, so the external angles add up to 6 x 120 + 3 x 60; subtracting 3x60 to find the difference gives 6x 120 = 720 degrees. Even if you exclude the three external angles of 60 degrees, you still have aa total of 6 angles of 120 degrees, or 720 degrees, giving a difference of 540 degrees

(2) You didn't say it was a right angled triangle, in which case it doesn't have a hypotenuse! However

If we assume it is then (2rt5)^2 + 5^2 = 20 + 25 = 45, so none of the answers is correct - I would guess that answer(c) is a typo

(3( Complementary angles add up to 90 degrees, so if the smaller angle is x degrees, the larger is 5x degrees, so 6x = 90 so x = 15, so the angles are 15 degrees and 75degrees

(4) Suppose the length of the diagonal is L, then by the Theorem of Pythogoras L^2 = 10^2 + 4^2

so L^2 = 100 + 16 = 116 = 4 x 29; that means (taking a square root) that L = sqrt(4 x 29) = sqrt(4) x sqrt(29) = 2rt29

1) Equilateral = equiangles

Each internal angle = 180/3 = 60

Each external angle = (180 - 60) = 120

Sum exterior - sum interior = 3*120 - 3*60 = 3*60 = 180 <<<

2) sqrt( (2*sqrt(5))^2 + 5^2)

sqrt(4*5 + 25)

sqrt(45) <<<

3)x + 5*x = 90

x = 15

Large angle = 5*x = 75 <<<

4) sqrt(10^2 + 4^2) = sqrt(116)

= sqrt(4*29)

= 2*sqrt(29) <<<