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3 years ago

Angle 3 is equal to angle ____

Mathematics

2 answers:

Misha Larkins [42]3 years ago

6 0

Alternate interior angles are congruent. So, angle 3 = angle 7.

We see that vertical angles are congruent. So, angle 3 also = angle 5.

Alternate exterior angles are congruent.

So, angle 3 also = angle 1.

Nikitich [7]3 years ago

5 0

Answer:

Step-by-step explanation:

they are across from eachother

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Answer:

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2 years ago

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Answer:

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3 years ago

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Answer:

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Arisa [49]

Multiply both the numerator and denominator by $2+\sqrt3$ , which is called the "conjugate" of $2-\sqrt3$ :

$\dfrac{5+\sqrt3}{2-\sqrt3}\cdot\dfrac{2+\sqrt3}{2+\sqrt3}$

Why do we pick this number? Recall the difference of squares factorization:

$a^2-b^2=(a-b)(a+b)$

Now replace $a=2$ and $b=\sqrt3$ . Then

$(2-\sqrt3)(2+\sqrt3)=2^2-(\sqrt3)^2=4-3=1$

So in your fraction, you end up with

$\dfrac{5+\sqrt3}{2-\sqrt3}=\dfrac{(5+\sqrt3)(2+\sqrt3)}1=(5+\sqrt3)(2+\sqrt3)$

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