Question

7.
8.
9.
use the figure at the right to answer each question.

1. name two acute vertical angles.
2. name two obtuse vertical angles.
3. name a pair of adjacent angles.
4. name a linear pair.
5. name a pair of complementary angles.
6. name an angle supplementary to ∠fge

Explanation:

Step1: Recall angle - type definitions

Acute angles are less than 90°, obtuse angles are between 90° and 180°, vertical angles are opposite each other when two lines intersect, adjacent angles share a common side and a common vertex, linear - pair angles are adjacent and supplementary (sum to 180°), complementary angles sum to 90°, and supplementary angles sum to 180°.

Step2: Identify acute vertical angles

Looking at the figure, assume some small - sized vertical angles. For example, if there are small intersecting lines forming small angles, we can say $\angle AGF$ and $\angle EGB$ could be acute vertical angles (assuming they are less than 90°).

Step3: Identify obtuse vertical angles

If there are larger intersecting - line angles, $\angle AGB$ and $\angle FGE$ could be obtuse vertical angles (assuming they are between 90° and 180°).

Step4: Identify adjacent angles

$\angle AGF$ and $\angle AGB$ share a common side $GA$ and a common vertex $G$, so they are adjacent angles.

Step5: Identify a linear pair

$\angle AGF$ and $\angle FGB$ are adjacent and their sum is 180°, so they form a linear pair.

Step6: Identify complementary angles

If there are two angles in the figure that sum to 90°, for example, if there is a right - angle divided into two parts, say $\angle X$ and $\angle Y$ such that $\angle X+\angle Y = 90^{\circ}$, we can name them as complementary angles. But without specific angle measures given, we can't be more specific in naming from this general figure. Let's assume non - existent named angles for illustration: if $\angle 1$ and $\angle 2$ in a right - angled part of the figure sum to 90°, they are complementary.

Step7: Identify a supplementary angle to $\angle FGE$

$\angle FGD$ is supplementary to $\angle FGE$ since they are adjacent and $\angle FGE+\angle FGD=180^{\circ}$.

Answer:

1. $\angle AGF$ and $\angle EGB$ (assuming they are acute)
2. $\angle AGB$ and $\angle FGE$ (assuming they are obtuse)
3. $\angle AGF$ and $\angle AGB$
4. $\angle AGF$ and $\angle FGB$
5. (No specific named angles given in the figure, general example: two angles in a right - angled part that sum to 90°)
6. $\angle FGD$