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AlladinOne [14]
3 years ago
11

If m∠1 =63° , find m∠2 and m∠3 by calculation

Mathematics
1 answer:
Neko [114]3 years ago
6 0
Since ∠1 is 63 than ∠2 is 63 too because they are alternate interior. To find ∠3 you subtract 180 by the measure of ∠2 because both of these angles create a straight line.

180 - 63 = ∠3
117 = ∠3

Hope this helps :)
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What is the exact value of cos (67.5°)?
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first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.

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cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill

cos(67.5^o)\implies cos\left( \frac{135^o}{2} \right)\implies \pm \sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}} \\\\\\ \sqrt{\cfrac{ ~~ \frac{2-\sqrt{2}}{2} ~~ }{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{\sqrt{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{2}

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2 years ago
Matthew wants to buy a new pair of jeans. If the jeans were originally $65.00, but are on sale with a 10% discount, how much wil
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