Interior angles of quadrilateralsthe sum of the four angles of any quadrilateral is 360

Mathematics

1 answer:

MaRussiya [10]2 years ago

8 0

Answers:
angle x= E. 118°
angle m= 131°

explanation:
the sum of the four angles of any quadrilateral
is 360

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nikdorinn [45]

Answer:

$\angle ABC=20^{\circ}$

Step-by-step explanation:

Since each side of a line is 180 degrees, we can write the following system of equations:

$\begin{cases}2x+12y+x+2y=180,\\x+2y+8y-4x=180\end{cases},\\\begin{cases}3x+14y=180,\\-3x+10y=180\end{cases}$

Add both equations to solve for $y$ :

$24y=360,\\y=\frac{360}{24}=15$

Now substitute $y=15$ into $3x+14y=180$ to solve for $x$ :

$3x+14(15)=180,\\3x=-30,\\x=-10$

Finish by substituting both variables to solve for $\angle ABC$ :

$\angle ABC=x+2y,\\\angle ABC=-10+2(15),\\\angle ABC=-10+30=\boxed{20^{\circ}}$

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2 years ago

You have 8 times as many dimes as nickels. You have 18 dimes

fenix001 [56]

Answer:

$1.70

Step-by-step explanation:

Let the number of nickels be $x$ .

Thus, by the problem statement, the number of dimes is [/tex] 8 \cdot x = 8x. [/tex]

Therefore, there are $8x + x = 9$ coins in total. To find what $x$ is, we need to solve the equation $9x = 18.$ This can be done by dividing both sides by $9$ which gives $x=2$ . Plugging these values in tells us that there are $2$ nickels and $16$ dimes. (Test it out!) Thus, the nickels are worth $2 \cdot 5 = 10$ cents and the dimes are worth $16 \cdot 10 = 160$ cents, so in all, you have $10 + 160 = 170$ cents which is $1.70.