Question

What is the value of x?

Answer 1

We are given the values of two angles along two parallel lines.

The relationship of these angles tells us that if we add these two angles, they should equal 180°. So then we can set that equation up:

$(2x+24)+x=180$

And then we solve for x:

$(2x+24)+x=180$

$3x+24=180$

$3x=156$

$x=52$

So now that we know the value of x is 52, we know that the angle whose value is x, is 52°.

To solve for the other angle, we must plug in 52 for x:

$2x+24$

$2(52)+24$

$104+24=128$

And now we know that the value of the other angle is 128°.

Answer 2

Since this is a parallelogram and the angles are adjacent to one another, a theorem will prove that the sum of these two angles would equal 180°

Therefore, we can set up this equation:

(2x + 24) + x = 180 ⇒ Remove parentheses

2x + 24 + x = 180 ⇒ Combine like terms

3x + 24 = 180 ⇒ Subtract 24 from both sides

3x = 156 ⇒ Divide both sides by 3

x = 52°