show all of your work on this worksheet and then enter your answers on formative. both are required in order to receive credit for the assignment. 1) the following angles have what type of relationship? a. the angle measure is: b. x = 2) solve for x: 12x + 10 5x + 31 3) two lines intersect, forming vertical angles a and b.

Question

show all of your work on this worksheet and then enter your answers on formative. both are required in order to receive credit for the assignment. 1) the following angles have what type of relationship? a. the angle measure is: b. x = 2) solve for x: 12x + 10 5x + 31 3) two lines intersect, forming vertical angles a and b. <a = 4x - 10 and <b = 2x + 26. what is the measure of angle b? 4) given: <1 and <2 are vertical angles. prove: <1 is congruent to <2. statements reasons points a, b, and c are collinear and b is between a and c. given ab = 12 and ac = 19, what is bc? (hint: draw a)

Accepted Answer

# Explanation:
## Step1: Identify vertical - angle property
Vertical angles are equal. For problem 2), since the two angles are vertical angles, we set up the equation $12x + 10=5x + 31$.
$12x+10 = 5x + 31$
## Step2: Solve the equation for x
Subtract $5x$ from both sides: $12x-5x+10=5x - 5x+31$, which simplifies to $7x+10 = 31$. Then subtract 10 from both sides: $7x+10 - 10=31 - 10$, getting $7x=21$. Divide both sides by 7: $x=\frac{21}{7}=3$.
## Step3: For problem 3)
Since $\angle A$ and $\angle B$ are vertical angles, $\angle A=\angle B$. So we set up the equation $4x - 10=2x + 26$.
$4x-10 = 2x + 26$
## Step4: Solve the equation for x in problem 3)
Subtract $2x$ from both sides: $4x-2x-10=2x-2x + 26$, which gives $2x-10 = 26$. Add 10 to both sides: $2x-10 + 10=26+10$, getting $2x=36$. Divide both sides by 2: $x = 18$.
## Step5: Find the measure of $\angle B$
Substitute $x = 18$ into the expression for $\angle B$: $\angle B=2x+26=2	imes18 + 26=36 + 26=62$.
## Step6: For problem 4)
| Statements | Reasons |
|--|--|
| $\angle1$ and $\angle2$ are vertical angles | Given |
| $\angle1+\angle A = 180^{\circ}$ | Linear - pair postulate |
| $\angle2+\angle A = 180^{\circ}$ | Linear - pair postulate |
| $\angle1+\angle A=\angle2+\angle A$ | Substitution property of equality |
| $\angle1=\angle2$ | Subtraction property of equality (subtract $\angle A$ from both sides) |
| $\angle1\cong\angle2$ | Definition of congruent angles (angles with equal measures are congruent) |

# Answer:
2) $x = 3$
3) The measure of angle B is $62^{\circ}$
4) See the above - filled two - column proof.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Identify vertical - angle property

Step2: Solve the equation for x

Step3: For problem 3)

Step4: Solve the equation for x in problem 3)

Step5: Find the measure of $\angle B$

Step6: For problem 4)

Answer:

Statements	Reasons
$\angle1+\angle A = 180^{\circ}$	Linear - pair postulate
$\angle2+\angle A = 180^{\circ}$	Linear - pair postulate
$\angle1+\angle A=\angle2+\angle A$	Substitution property of equality
$\angle1=\angle2$	Subtraction property of equality (subtract $\angle A$ from both sides)
$\angle1\cong\angle2$	Definition of congruent angles (angles with equal measures are congruent)