Question

PLEASE HELP THE QUESTION IS BELOW!!

Answer 1

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 2

146°

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

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

Collect like terms

`15x - 2 + 2= 180`

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

`15x = 80`

Divide both sides of the equation by 15

`(15x)/(15) = (80)/(15)`

Calculate

`x = </strong><strong>1</strong><strong>2</strong><strong>`

Replacing value,

<C = 12x + 2

plug the value of X

`= 12 * 12 - 2`

Multiply the numbers

`= 144 + 2`

Calculate the difference

`= 146`

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!!