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klio [65]
3 years ago
13

How many degrees is angle y

Mathematics
2 answers:
Hatshy [7]3 years ago
7 0

<u>Answer:</u>

<h2>y = 39°</h2>

<u>Steps:</u>

w = 180 - (85+42) = 180 - 127 = 53°

y = 180 - (88+w)

y = 180 - (88+53)

y = 180 - 141

y = 39°

Verdich [7]3 years ago
3 0

Answer:

y = 39

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of both triangles , then

x = 42 + 85 = 127

and

y + 88 = 127 ( subtract 88 from both sides )

y = 39

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1. In ABC, A=45 degrees, B=75 degrees, and BC=12. What is the length of AB?
Aleksandr-060686 [28]

We know that sum of the interior angles of any triangle equal 180° :

So :

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_________________________________

According to the theorem of sinuses :

\frac{AB}{ \sin(C) } =  \frac{BC}{ \sin(A) } \\

\frac{AB}{ \sin(60) } =  \frac{12}{ \sin(45) } \\

\frac{AB}{ \frac{ \sqrt{3} }{2} } =  \frac{12}{ \frac{ \sqrt{2} }{2} } \\

Multiply \:  both \:  sides \:  by \:   \frac{ \sqrt{3} }{2}

AB =  \frac{24}{ \sqrt{2} } \times  \frac{ \sqrt{3} }{2} \\

AB =  \frac{12 \sqrt{3} }{ \sqrt{2} } \\

AB =  \frac{2 \times 6 \sqrt{3} }{ \sqrt{2} } \\

AB =  \frac{ ({ \sqrt{2} })^{2} \times 6 \sqrt{3}  }{ \sqrt{2} }  \\

AB =  \frac{ \sqrt{2} \times  \sqrt{2} \times 6 \sqrt{3}   }{ \sqrt{2} } \\

AB =  \frac{ \sqrt{2} \times  6 \sqrt{3}   }{1} \\

AB =  \sqrt{2} \times 6 \sqrt{3}

AB = 6 \sqrt{2 \times 3}

AB = 6 \sqrt{6}

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I think this is the correct answer.

And we're done.

Thanks for watching buddy good luck.

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