3. angles a and b are adjacent angles and are supplementary. the measure of ∠a is (3x + 10)°, and the measure of ∠b is (12x + 35)°.
a. write an equation that can be used to determine the value of x.

b. what is the value of x?

c. what is the measure of ∠a?

4. describe ∠coa in relation to ∠dob.

5. attend to precision ∠a is complementary to ∠b. the measure of ∠a is (8x + 12)°. the measure of ∠b is half the measure of ∠a. write an equation that can be used to determine the value of x. then solve for x.

for problems 6–7, use figure 4.

figure 4

6. describe the relationship between ∠boc and ∠cod. what is the sum of their angle measures?

7. describe the relationship between ∠aob and ∠cod. are their measures equal?

Question

3. angles a and b are adjacent angles and are supplementary. the measure of ∠a is (3x + 10)°, and the measure of ∠b is (12x + 35)°.
a. write an equation that can be used to determine the value of x.

b. what is the value of x?

c. what is the measure of ∠a?

4. describe ∠coa in relation to ∠dob.

5. attend to precision ∠a is complementary to ∠b. the measure of ∠a is (8x + 12)°. the measure of ∠b is half the measure of ∠a. write an equation that can be used to determine the value of x. then solve for x.

for problems 6–7, use figure 4.

figure 4

6. describe the relationship between ∠boc and ∠cod. what is the sum of their angle measures?

7. describe the relationship between ∠aob and ∠cod. are their measures equal?

Accepted Answer

### Problem 3
#### Part A
# Explanation:
## Step1: Recall supplementary angles
Supplementary angles sum to $180^\circ$. So, $\angle A + \angle B = 180^\circ$.
## Step2: Substitute angle measures
Substitute $\angle A=(3x + 10)^\circ$ and $\angle B=(12x + 35)^\circ$ into the equation: $(3x + 10)+(12x + 35)=180$.
# Answer:
$(3x + 10)+(12x + 35)=180$

#### Part B
# Explanation:
## Step1: Simplify the equation
Combine like terms: $3x+12x + 10 + 35=180$ → $15x+45 = 180$.
## Step2: Solve for $x$
Subtract 45 from both sides: $15x=180 - 45=135$. Divide by 15: $x=\frac{135}{15}=9$.
# Answer:
$x = 9$

#### Part C
# Explanation:
## Step1: Substitute $x = 9$ into $\angle A$'s formula
$\angle A=(3x + 10)^\circ$. Substitute $x = 9$: $3(9)+10=27 + 10=37$.
# Answer:
$\angle A = 37^\circ$

### Problem 4
# Brief Explanations:
$\angle COA$ and $\angle DOB$: Vertical angles are equal. $\angle DOB = 60^\circ$ (given). $\angle COA$ and $\angle DOB$ are vertical angles (formed by intersecting lines), so $\angle COA=\angle DOB = 60^\circ$, and they are equal (vertical angles).
# Answer:
$\angle COA$ is equal to $\angle DOB$ (they are vertical angles).

### Problem 5
# Explanation:
## Step1: Recall complementary angles
Complementary angles sum to $90^\circ$. $\angle B=\frac{1}{2}\angle A$, and $\angle A=(8x + 12)^\circ$, so $\angle B=\frac{1}{2}(8x + 12)^\circ=(4x + 6)^\circ$.
## Step2: Write the equation
$\angle A+\angle B = 90^\circ$ → $(8x + 12)+(4x + 6)=90$.
## Step3: Solve the equation
Combine like terms: $12x+18 = 90$. Subtract 18: $12x=72$. Divide by 12: $x = 6$.
# Answer:
Equation: $(8x + 12)+\frac{1}{2}(8x + 12)=90$ (or simplified $(8x + 12)+(4x + 6)=90$); $x = 6$

### Problem 6
# Brief Explanations:
$\angle BOC$ and $\angle COD$: They are adjacent angles forming a linear pair (since $B$, $O$, $D$ are on a straight line? Wait, no—looking at Figure 4, $\angle BOC$ and $\angle COD$ share a common side $OC$ and their non - common sides $OB$ and $OD$ form a straight line? Wait, actually, $\angle BOC$ and $\angle COD$ are adjacent and their sum is $180^\circ$ (linear pair). So their relationship is that they are supplementary (form a linear pair), and their sum is $180^\circ$.
# Answer:
$\angle BOC$ and $\angle COD$ are supplementary (form a linear pair), and their sum is $180^\circ$.

### Problem 7
# Brief Explanations:
$\angle AOB$ and $\angle COD$: $\angle AOB$ is a straight angle? No, $\angle AOB$ and $\angle COD$: Let's see, $\angle AOB$ and $\angle COD$ are vertical angles? Wait, in Figure 4, lines $AB$ (straight line) and $EC$ (intersecting at $O$)? Wait, $\angle AOB$ is a straight angle? No, $\angle AOB$ is a right angle? Wait, no—$\angle AOB$ and $\angle COD$: If $OA$ and $OE$ are symmetric, but actually, $\angle AOB$ and $\angle COD$ are vertical angles (formed by intersecting lines $AB$ and $EC$? Wait, no, looking at the figure, $\angle AOB$ and $\angle COD$ are vertical angles, so their measures are equal.
# Answer:
$\angle AOB$ and $\angle COD$ are vertical angles, and their measures are equal.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 3

Part A

Step1: Recall supplementary angles

Step2: Substitute angle measures

Step1: Simplify the equation

Step2: Solve for \(x\)

Step1: Substitute \(x = 9\) into \(\angle A\)'s formula

Answer:

Part B