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elena55 [62]
3 years ago
9

PLEASE HELP!!!

Mathematics
2 answers:
nika2105 [10]3 years ago
4 0

Answer:

x = 40

Step-by-step explanation:

x + 100 +  x = 180 {Straight line angles}

2x   + 100 = 180      {subtract 100 from both sides}

         2x = 180 - 100

         2x = 80      {Divide both sides by 2)

           x = 80/2

          x = 40

Yuki888 [10]3 years ago
3 0

Answer:

x=40

Step-by-step explanation:

2x+100=180

2x=180-100

2x=80

x=40

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Answer:  see proof below

<u>Step-by-step explanation:</u>

Given: cos 330 = \frac{\sqrt3}{2}

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Proof LHS → RHS:

LHS                          cos 165

Double-Angle:        cos (2 · 165) = 2 cos² 165 - 1

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Given:                        2 \cos^2 165  = \dfrac{\sqrt3}{2} + 1

                              \rightarrow 2 \cos^2 165  = \dfrac{\sqrt3}{2} + \dfrac{2}{2}

Divide by 2:               \cos^2 165  = \dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}

                             \rightarrow \cos^2 165  = \dfrac{2\sqrt3+4}{8}

Square root:             \sqrt{\cos^2 165}  = \sqrt{\dfrac{4+2\sqrt3}{8}}

Scratchwork:            \cos^2 165  = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2

                             \rightarrow \cos 165  = \pm \dfrac{\sqrt3+1}{2\sqrt2}

             Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

                             \rightarrow \cos 165  = - \dfrac{\sqrt3+1}{2\sqrt2}

LHS = RHS \checkmark

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I hope this helps you:) Please mark brainliest if correct:)

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