We are given the following diagram.

We want to determine which of the given statements is not true concerning $∠ A,$ $∠ B,$ and $∠ C .$ Let's analyze the statements one at a time.

Statement F

First, we will consider statement F.

$∠ B$ and $∠ C$ are obtuse angles.

Recall that obtuse angles are angles that measure more than $9 0^{\circ}$ but less than $18 0^{\circ} .$ Let's look at $∠ B$ and $∠ C .$

We can see that $∠ B$ and $∠ C$ are right angles. Since these angles have a measure of $9 0^{\circ},$ they are not obtuse. Therefore, statement F is not true.

Statement G

Now we will analyze statement G.

$∠ A$ and $∠ C$ are vertical angles.

When two lines or line segments intersect, vertical angles are formed on opposite sides of the point of intersection. To check whether $∠ A$ and $∠ C$ are vertical, let's take another look at the diagram.

Notice that $∠ A$ and $∠ C$ are on opposite sides of the point of intersection of two lines. This means that these angles are vertical, so statement G is true.

Statement H

Next, we will consider statement H.

$∠ A$ and $∠ B$ are alternate interior angles.

Notice that in the diagram, we have two parallel lines that are cut by a transversal. Recall that alternate interior angles are interior angles that lie on opposite sides of the transversal. Looking at the diagram, we can determine whether $∠ A$ and $∠ B$ are alternate interior angles.

Indeed, $∠ A$ and $∠ B$ are interior angles that lie on opposite sides of the transversal. Therefore, these angles are alternate interior angles, and statement H is true.

Statement I

Finally, we will analyze statement I.

$∠ A$ and $∠ C$ are congruent.

Since statement G is true, we know that $∠ A$ and $∠ C$ are vertical angles. Recall that vertical angles are always congruent. This means that $∠ A$ and $∠ C$ are congruent and statement I is also true.

Conclusion

We found that only statement F is not true.

Exercise