Question

whats the measurement for ENV

Answer 1

C; Since <RNA and <ENV are vertical angles, that means they are equal to each other. To solve this, set both equations equal to each other and solve for x.

8x+12=5x+57

3x+12=57

3x=45

x=15

Now that we have x just plug it in for the desired angle.

5(15)+57

75+57

132

<ENV is 132 degrees. <RNA, as mentioned, will be the same since the two angles are vertical.

Answer 2

The correct option is Option C: The measure of ∠ENV = 132°

What is vertical angle?

When two lines intersect each other at one point, then two opposite angles formed are called vertical angles.

When two lines cut each other, then two pairs of vertical angles are formed.

Here, Line RV and AE intersect each other at point N.

The vertical angle pairs formed are ∠RNA and ∠ENV ;  ∠RNE  and ∠ANV

So using vertical angle theorm,

two vertical angles will be equal.

∠RNA=∠ENV ;  

∠RNE=∠ANV

So, here

∠RNA=(8x+12)°

∠ENV=(5x+57)°

As ∠RNA=∠ENV  (as two vertical angles will be equal)

⇒(8x+12)°=(5x+57)°

⇒8x-5x=57°-12°

⇒3x=45°

⇒x=45°/3

⇒x=15°

∠ENV=(5x+57)°=(5*15°)+57°=75°+57°=132°

Therefore, the measure of ∠ENV is 132°.

Learn more about vertical angle

here: https://brainly.com/question/14362353

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