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3 years ago

What smaller angle is coterminal with 573°

Mathematics

1 answer:

Kobotan [32]3 years ago

5 0

The positive coterminal angle is 213° and negative coterminal angle is -147° and -507°

<u>Explanation:</u>

Coterminal angles are two angles that are drawn in the standard position (so their initial sides are on the positive x-axis) and have the same terminal side

In other words, two angles are coterminal when the angles themselves are different, but their sides and vertices are identical.

Another way to describe coterminal angles is that they are two angles in the standard position and one angle is a multiple of 360 degrees larger or smaller than the other. That is, if angle A has a measure of M degrees, then angle B is co-terminal if it measures M +/- 360n, where n = 0, 1, 2, 3, ...

So,

When angle is 573° then the coterminal angle is

573° - 360 (1) = 213°

573° - 360(2) = -147°

573° - 360 (3) = -507°

Therefore, positive coterminal angle is 213° and negative coterminal angle is -147° and -507°

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Experimentally verify sum of three angles of an triangle is 180⁰.

svetlana [45]

Draw line a through points A and B. Draw line b through point C and parallel to line a.

Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'.

It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees.

Thus <)ABC + <)BCA + <)CAB = 180 degrees.

Lemma

If ABCD is a quadrilateral and <)CAB = <)DCA then AB and DC are parallel.

Proof

Assume to the contrary that AB and DC are not parallel.

Draw a line trough A and B and draw a line trough D and C.

These lines are not parallel so they cross at one point. Call this point E.

Notice that <)AEC is greater than 0.

Since <)CAB = <)DCA, <)CAE + <)ACE = 180 degrees.

Hence <)AEC + <)CAE + <)ACE is greater than 180 degrees.

Contradiction. This completes the proof.

Definition

Two Triangles ABC and A'B'C' are congruent if and only if

|AB| = |A'B'|, |AC| = |A'C'|, |BC| = |B'C'| and,

<)ABC = <)A'B'C', <)BCA = <)B'C'A', <)CAB = <)C'A'B'.

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One bottle contains 341 ml of juice. Céline buys 2 cases of 24 bottles of juice. Nicole buys 3 cases of 12 bottles of juice. Who

Helga [31]

Answer: Celine, 4092 ml

Step-by-step explanation:

Given

1 bottle contains 341 ml Juice

Celine buys 2 cases of 24 bottles i.e. a total of 48 bottles

Nicole buys 3 cases of 12 bottles i.e. a total of 36 bottles

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Amount of Juice Nicole has

$\Rightarrow 36\times 341=12,276\ ml$

Thus, Celine has more juice than Nicole

$\Rightarrow 16,368-12,276=4092\ ml$

Celine has 4092 ml more than Nicole

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