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deepeshvcd6273

Answer:

Step-by-step explanation:

B=3x-2

C=12x+2

D=B=3x-2 (Vertically opposite angles)

A=?

Now; we know, A+B+C+D=360 deg.

=>A=360-(B+C+D)

  =360-(3x-2+12x+2+3x-2)

  =360-(18x-2) ----[1]

B+C=180 deg. (linear pair)

=> 3x-2+12x+2=180

=> 15x=180

=> x=180/15

   =12 ---[2]

subsitute [2] in [1];

=> A= 360-(18x-2)

   = 360-(18*12-2)

   = 360-(116-2)

   = 360-214

   = 146 deg.

   

So, the correct answer is (D).

Hope the answer is useful.  

Answer:

146°

Step-by-step explanation:

Given,

< B = 3x - 2

<C = 12x + 2

Let's find the value of X

<B + < C = 180° ( sum of angle in straight line)

plug the values

[tex]3x - 2 + 12x + 2 = 180[/tex]

Collect like terms

[tex]15x - 2 + 2= 180[/tex]

Since, two opposites add up to zero, remove them from the equation

[tex]15x = 80[/tex]

Divide both sides of the equation by 15

[tex] \frac{15x}{15} = \frac{80}{15} [/tex]

Calculate

[tex]x = 12[/tex]

Replacing value,

<C = 12x + 2

plug the value of X

[tex] = 12 \times 12 - 2[/tex]

Multiply the numbers

[tex] = 144 + 2[/tex]

Calculate the difference

[tex] = 146[/tex]

The measure of <C is 146°

Here,

<A = < C ( being vertically opposite angles)

Vertically opposite angles are always equal.

<A = 146

Hence, Option D is the correct answer.

Hope this helps...

Best regards!!

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