Question

use the following diagram to state if the following are true in problems #1 - 8. 1. ∠fbc is an obtuse angle. a. yes b. no 2. (overrightarrow{ca}) a. yes b. no 3. (overrightarrow{bd}) a. yes b. no 4. ∠afb a. yes b. no 5. ∠abg is a right angle. a. yes b. no 6. (overline{ab}congoverline{bc}) a. yes b. no 7. ∠gbd+∠dbe + ∠ebc=∠gbc a. yes b. no 8. fb + fd = bd a. yes b. no

Explanation:

Step1: Recall obtuse - angle definition

An obtuse angle is greater than 90° and less than 180°. $\angle FBC$ is less than 90°, so it is not obtuse.

Step2: Check line - segment notation

$\overrightarrow{CA}$ is not shown in the diagram.

Step3: Check line - segment notation

$\overrightarrow{BD}$ is shown in the diagram.

Step4: Check angle notation

$\angle AFB$ is shown in the diagram.

Step5: Recall right - angle definition

A right angle is 90°. $\angle ABG$ has a right - angle symbol, so it is a right angle.

Step6: Check line - segment congruence

There is no indication that $\overline{AB}\cong\overline{BC}$ in the diagram.

Step7: Recall angle - addition postulate

By the angle - addition postulate, $\angle GBD+\angle DBE+\angle EBC=\angle GBC$.

Step8: Check line - segment addition

$FB + FD
eq BD$ as $F$, $B$, and $D$ are not collinear in that order for this addition to hold.

Answer:

1. b. No
2. b. No
3. a. Yes
4. a. Yes
5. a. Yes
6. b. No
7. a. Yes
8. b. No