part a
indicate whether each statement is true or false.

| the sum of the measures of $\angle abg$ and $\angle cba$ is always equal to $90^\circ$. | true | false |
| the measure of $\angle cbg$ is always equal to the measure of $\angle fbd$. | | |
| the sum of the measures of $\angle dbc$, $\angle cba$, and $\angle abg$ is always equal to $180^\circ$. | | |
| the measure of $\angle gbf$ is always equal to the measure of $\angle ebd$. | | |
| the sum of the measures of $\angle cba$, $\angle fbg$, and $\angle ebd$ is always equal to $180^\circ$. | | |
| the sum of the measures of $\angle abg$, $\angle gbf$, $\angle fbe$, and $\angle dbc$ is always equal to $360^\circ$. | | |

art b
and $m\angle gbf = 110^\circ$.

Question

part a
indicate whether each statement is true or false.

| the sum of the measures of $\angle abg$ and $\angle cba$ is always equal to $90^\circ$. | true | false |
| the measure of $\angle cbg$ is always equal to the measure of $\angle fbd$. |  |  |
| the sum of the measures of $\angle dbc$, $\angle cba$, and $\angle abg$ is always equal to $180^\circ$. |  |  |
| the measure of $\angle gbf$ is always equal to the measure of $\angle ebd$. |  |  |
| the sum of the measures of $\angle cba$, $\angle fbg$, and $\angle ebd$ is always equal to $180^\circ$. |  |  |
| the sum of the measures of $\angle abg$, $\angle gbf$, $\angle fbe$, and $\angle dbc$ is always equal to $360^\circ$. |  |  |

art b
and $m\angle gbf = 110^\circ$.

Accepted Answer

# Explanation:
## Statement 1: The sum of the measures of ∠ABG and ∠CBA is always equal to 90°
There is no information given that these two angles are complementary (sum to 90°). So this statement is false.
## Statement 2: The measure of ∠CBG is always equal to the measure of ∠FBD
There is no information given that these two angles are equal. So this statement is false.
## Statement 3: The sum of the measures of ∠DBC, ∠CBA, and ∠ABG is always equal to 180°
There is no information given that these three angles form a straight - line (sum to 180°). So this statement is false.
## Statement 4: The measure of ∠GBF is always equal to the measure of ∠EBD
There is no information given that these two angles are equal. So this statement is false.
## Statement 5: The sum of the measures of ∠CBA, ∠FBG, and ∠EBD is always equal to 180°
There is no information given that these three angles form a straight - line (sum to 180°). So this statement is false.
## Statement 6: The sum of the measures of ∠ABG, ∠GBF, ∠FBE, and ∠DBC is always equal to 360°
There is no information given that these four angles form a full - circle (sum to 360°). So this statement is false.

# Answer:
| Statement | True | False |
|---|---|---|
| The sum of the measures of ∠ABG and ∠CBA is always equal to 90° |  | ✓ |
| The measure of ∠CBG is always equal to the measure of ∠FBD |  | ✓ |
| The sum of the measures of ∠DBC, ∠CBA, and ∠ABG is always equal to 180° |  | ✓ |
| The measure of ∠GBF is always equal to the measure of ∠EBD |  | ✓ |
| The sum of the measures of ∠CBA, ∠FBG, and ∠EBD is always equal to 180° |  | ✓ |
| The sum of the measures of ∠ABG, ∠GBF, ∠FBE, and ∠DBC is always equal to 360° |  | ✓ |

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QUESTION IMAGE

Question

Explanation:

Statement 1: The sum of the measures of ∠ABG and ∠CBA is always equal to 90°

Statement 2: The measure of ∠CBG is always equal to the measure of ∠FBD

Statement 3: The sum of the measures of ∠DBC, ∠CBA, and ∠ABG is always equal to 180°

Statement 4: The measure of ∠GBF is always equal to the measure of ∠EBD

Statement 5: The sum of the measures of ∠CBA, ∠FBG, and ∠EBD is always equal to 180°

Statement 6: The sum of the measures of ∠ABG, ∠GBF, ∠FBE, and ∠DBC is always equal to 360°

Answer:

the sum of the measures of $\angle abg$ and $\angle cba$ is always equal to $90^\circ$.	true	false
the measure of $\angle cbg$ is always equal to the measure of $\angle fbd$.
the sum of the measures of $\angle dbc$, $\angle cba$, and $\angle abg$ is always equal to $180^\circ$.
the measure of $\angle gbf$ is always equal to the measure of $\angle ebd$.
the sum of the measures of $\angle cba$, $\angle fbg$, and $\angle ebd$ is always equal to $180^\circ$.
the sum of the measures of $\angle abg$, $\angle gbf$, $\angle fbe$, and $\angle dbc$ is always equal to $360^\circ$.

Statement	True	False
The measure of ∠CBG is always equal to the measure of ∠FBD		✓
The sum of the measures of ∠DBC, ∠CBA, and ∠ABG is always equal to 180°		✓
The measure of ∠GBF is always equal to the measure of ∠EBD		✓
The sum of the measures of ∠CBA, ∠FBG, and ∠EBD is always equal to 180°		✓
The sum of the measures of ∠ABG, ∠GBF, ∠FBE, and ∠DBC is always equal to 360°		✓