Question

Four angles are formed by the intersection of these lines.
Choose the three true statements.
Pls help I’ve been stuck on this for a long time plz

Answer 1

So the three true statements would be
The bottom far left m<120
The top right corner m<2 =180-120
And the top left corner m<1 and m<2 are adjacent

Answer 2

The three true statements are:

∠1 and ∠2 are adjacent angles.

m∠2 = 180° - 120°.

m∠1 = 120° because ∠1 and the 120° angle are vertical angles.

How do we determine the angles when two lines intersect?

• Adjacent Angles: Angles on the same side of one line are adjacent angles. Their sum = 180°.

• Vertical angles: Angles opposite each other are vertical angles. They are always equal.

How do we solve the given question?

We can see that ∠1 and ∠2 are on the same side so they are adjacent angles.

Also, ∠2 and 120° angles are on the same side so they are adjacent angles. Since they are adjacent, we can say that:

∠2 + 120° = 180°.

or, ∠2 = 180° - 120° = 60°

∠1 and the 120° are opposite to each other, so they are vertical angles.

Since they are vertical, ∠1 = 120° ≠ 180° -  120°, also we have discovered the value of ∠1.

Now we can also see that ∠1 ≠ ∠2

After all this calculation, we can say that the three true statements are:

∠1 and ∠2 are adjacent angles.

m∠2 = 180° - 120°.

m∠1 = 120° because ∠1 and the 120° angle are vertical angles.

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