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Alina [70]
2 years ago
13

Two angles are vertical angles. One angle is ( 8x + 15 ) and the other angle is 143. Solve for x.

Mathematics
1 answer:
sineoko [7]2 years ago
5 0

Answer:

x = 16

Step-by-step explanation:

Verticle angles are always congruent, so:

(8x + 15) = 143

Now, we can solve to isolate x:

8x + 15 - 15 = 143 - 15  (subtract 15 from both sides)

8x/8 = 128/8                (divide both sides by 8)

x = 16

You can always plug in the value of x to the original equation to check your answer:

8(16) + 15 = 143

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Find the area of the polygon defined by the coordinates (0,-5),(-5,0),(-15,-20),and(-20,-15)
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Area of the polygon defined by the given points is 62.5 sq units

Step-by-step explanation:

Step 1 :    

Let P be the point (-5,0)  Q = (0,-5), R = (-15,-20) and S = (20,-15)

We have to to find the area of the polygon PQRS

Step 2 :

The area of polygon given the vertices (x(x_{1} ,y_{1} ), (x_{2} ,y_{2})  ... (x_{n} ,y_{n} ) is given by

Area  = mod ( (x_{1} y_{2}  - y_{1}x_{2}) + (x_{2} y_{3}  - y_{2}x_{3}) + ... (x_{n} y_{1}  - y_{n}x_{1}) ) ÷ 2

Where  x_{n} is the vertex n's x coordinate , y_{n} is the vertex n's y coordinate

Substituting the corresponding values ,

Area of PQRS = mod ( (25 - 0)+ (0-75) +(300-300) +( 0-75)  ) ÷ 2

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Step 3 :    

Answer :

Area of the polygon defined by the given points is 62.5 sq units

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