# ∠a and ∠b are vertical angles with m∠a = x and m∠b = 4x – 30. what is m∠a?

∠a and ∠b are vertical angles with m∠a = x and m∠b = 4x - 30. what is m∠a?

## This Post Has 12 Comments

1. Expert says:

step-by-step explanation:

2. fatboi82 says:

g

step-by-step explanation:

3. hiitslillyhere says:

$x = 4x -30$

We can solve for x subtracting x on both sides:

$x-x= 4x-x-30$

And then we can add 30 in both sides:

$30= 3x$

And dividing both sides by 3 we got:

$x = 10$

Step-by-step explanation:

For this case we know the measure of two angles:

$m <A = x$

$m<B = 4x-30$

And we know that both angles are vertical and by definition vertical angles are the angles opposite each other when two lines cross.

For this case since both angles are vertical we have the property that:

$m<A = m<B$

And replacing what we got we have:

$x = 4x -30$

We can solve for x subtracting x on both sides:

$x-x= 4x-x-30$

And then we can add 30 in both sides:

$30= 3x$

And dividing both sides by 3 we got:

$x = 10$

4. taten1701 says:

4x-30=180
180-30
4x=150
150/4
37.5
x=37.5

5. bearbri4520 says:

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always congruent to one another

in this problem

∠A and ​ ∠B ​ are vertical angles

so

∠A=∠B ​

we have

∠A=$x\°$

∠B=$(5x-80)\°$

equate angle A and angle B

$x=5x-80$

solve for x

$5x-x=80$

$4x=80$

$x=20\°$

therefore

the measure of angle A is $20\°$

6. inneedofhelp6237 says:

we know that

Vertical angles are congruent angles opposite each other where two lines cross

so

in this problem

m∠A=m∠B

so

substitute the values

$x=3x-60\\3x-x=60\\2x=60\\x=60/2\\x=30\°$

therefore

The measure of angle A is $30\°$

7. zitterkoph says:

m∠A=30°

Step-by-step explanation:

we know that

Vertical Angles are the angles opposite each other when two lines cross.

Vertical angles always are congruent

In this problem

m∠A=m∠B ----> by vertical angles

we have

m∠A=x

m∠B=3x-60

substitute

$3x-60=x$

Solve for x

$3x-x=60$

$2x=60$

$x=30$

therefore

m∠A=30°

8. devenybates says:

m∠A=10°

Step-by-step explanation:

we know that

Vertical angles are the angles opposite each other when two lines cross. The angles are congruent.

so

In this problem we have

m∠A=m∠B

substitute the given values

$x=4x-30$

Solve for x

$4x-x=30\\3x=30\\x=10$

Find the measure of angle A

m∠A=x

substitute the value of x

m∠A=10°

9. nockturnal1993 says:

Angle A would be anything that Angle B is. If the angles are vertical then they are always congruent.

10. nijanicole164 says:

20 degrees
vertical angles are equal, so 5x-80=x
solve for x and you get 20

11. Expert says:

l.jnl.j/n.m,lm,

step-by-step explanation:

12. zivicion says:

∠A and ∠B are vertical angles
so
∠A =∠B
x = 4x - 30
4x - x = 30
3x = 30
x = 10

m<A= x = 10