Question

If m∠4 = (3x)° and m∠8 = (x + 40)°, what is the measure of ∠4? Angles 4 and 8 being vertical.

Answer 1

If the angles are vertical then there sum would be equal.
3x = x + 40
3x - x = 40
2x = 40
x = 20

Now, m<4 = 3x = 3(20) = 60

In short, Your Answer would be 60

Hope this helps!

Answer 2

the measure of ∠4 is 60°

Explanation:

Two angles are Vertical angles when they are opposite to each other and are congruent.

As per the statement:

If m∠4 = (3x)° and m∠8 = (x + 40)°

Since, angles 4 and 8 being vertical.

then by definition we have;

`m\angle 4=m\angle 8`

Substitute the given values we have;

`3x = x+40`

Subtract x from both sides we have;

`2x=40`

Divide both sides by 2 we have;

x = 20

Substitute the value of x in m∠4 = (3x)°

then;

m∠4 = (3(20))° = 60°

Therefore, the measure of ∠4 is 60°