choose yes or no to indicate whether each equation is correc
a. $m\angle abc = 97\degree$ \bigcirc yes
b. $m\angle abc = 83\degree$ \bigcirc yes
c. $m\angle 1 = 97\degree$ \bigcirc yes
d. $m\angle 1 = 135\degree$ \bigcirc yes

Question

Accepted Answer

### Part a
# Explanation:
## Step1: Recall triangle angle sum
The sum of angles in a triangle is $180^\circ$. In $\triangle ABC$, we know $\angle A = 52^\circ$ and $\angle C = 45^\circ$.
## Step2: Calculate $\angle ABC$
$m\angle ABC=180^\circ - 52^\circ - 45^\circ = 83^\circ$. So $m\angle ABC = 97^\circ$ is incorrect.
# Answer: No

### Part b
# Explanation:
## Step1: Use triangle angle sum
Sum of angles in $\triangle ABC$ is $180^\circ$. Given $\angle A = 52^\circ$, $\angle C = 45^\circ$.
## Step2: Compute $\angle ABC$
$m\angle ABC = 180^\circ-52^\circ - 45^\circ=83^\circ$. So this equation is correct.
# Answer: Yes

### Part c
# Explanation:
## Step1: Identify linear pair
$\angle 1$ and $\angle ABC$ form a linear pair, so their sum is $180^\circ$.
## Step2: Calculate $m\angle 1$
We found $m\angle ABC = 83^\circ$, so $m\angle 1=180^\circ - 83^\circ = 97^\circ$. This equation is correct.
# Answer: Yes

### Part d
# Explanation:
## Step1: Use linear pair property
$\angle 1$ and $\angle ABC$ are supplementary ($180^\circ$). We know $m\angle ABC = 83^\circ$.
## Step2: Find $m\angle 1$
$m\angle 1 = 180^\circ-83^\circ = 97^\circ
eq135^\circ$. So this equation is incorrect.
# Answer: No

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QUESTION IMAGE

Question

Explanation:

Part a

Step1: Recall triangle angle sum

Step2: Calculate \(\angle ABC\)

Step1: Use triangle angle sum

Step2: Compute \(\angle ABC\)

Step1: Identify linear pair

Step2: Calculate \(m\angle 1\)

Answer:

Part b