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3 years ago

Solve for x! Please help!

Mathematics

1 answer:

erica [24]3 years ago

3 0

Answer:

Step-by-step explanation:

ΔADC and ΔCDB are similar (AA). Therefore the sides are in proportion:

$\dfrac{AD}{DC}=\dfrac{DC}{DB}$

We have AD = 16, DC = x, DB = 9. Substitute:

$\dfrac{16}{x}=\dfrac{x}{9}$ <em>cross multiply</em>

$x^2=(16)(9)\to x=\sqrt{(16)(9)}\\\\x=\sqrt{16}\cdot\sqrt9\\\\x=4\cdot3\\\\x=12$

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3 years ago

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3 years ago

Find the measure of each of the angles. Don’t forget to label your answer

user100 [1]

Answer:

$a=125^o$

$b=55^o$

$c=55^o$

$d=55^o$

$e=125^o$

$f=55^o$

Step-by-step explanation:

step 1

Find the value of x

we know that

$(2x+25)^o=(x+75)^o$ ----> by alternate interior angles

solve for x

Group terms

$2x-x=75-25$

$x=50$

step 2

Find the measure of angle a

we know that

$a=(x+75)^o$ ----> by vertical angles

substitute the value of x

$a=(50+75)=125^o$

step 3

Find the measure of angle b

we know that

$a+b=180^o$ ----> by supplementary angles (form a linear pair)

we have

$a=125^o$

substitute

$125^o+b=180^o$

$b=180^o-125^o=55^o$

step 4

Find the measure of angle c

we know that

$c=b$ ----> by vertical angles

we have

$b=55^o$

therefore

$c=55^o$

step 5

Find the measure of angle d

we know that

$d=b$ ----> by corresponding angles

we have

$b=55^o$

therefore

$d=55^o$

step 6

Find the measure of angle e

we know that

$e=a$ ----> by alternate exterior angles

we have

$a=125^o$

therefore

$e=125^o$

step 7

Find the measure of angle f

we know that

$f=d$ ----> by vertical angles

we have

$d=55^o$

therefore

$f=55^o$

4 0

2 years ago