Question

∠A and ​ ∠B ​ are vertical angles with  m∠A=x and  m∠B=4x−30 . What is m∠A ? Enter your answer in the box.

Answer 1

First off, if they’re vertical angles, they have to be congruent. So set the equation up as x=4x-30. Then solve and get the answer of x=10. Therefore your angle measure is 10 degrees

Answer 2

`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`

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`