QuestionFind the measure of $\angle 2$ given that $\mathrm{m} \angle 1=(2 x+29)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-17)^{\circ}$ , where they are vertical angles.

Studdy Solution

STEP 1

Assumptions1. $\angle1$ and $\angle$ are vertical angles. . The measure of $\angle1$ is given by $(x+29)^\circ$ .
3. The measure of $\angle$ is given by $(3x-17)^\circ$ .
4. Vertical angles are equal in measure.

STEP 2

We know that vertical angles are equal, so we can set the measures of $\angle1$ and $\angle2$ equal to each other and solve for $x$ .
$(2x+29)^\circ = (x-17)^\circ$

STEP 3

First, we can get rid of the degree symbol since it's the same on both sides.
$2x+29 =3x-17$

STEP 4

Next, we can rearrange the equation to isolate $x$ on one side. We can do this by subtracting $2x$ from both sides.
$29 = x -17$

STEP 5

Then, we add $17$ to both sides to solve for $x$ .
$x =29 +17$

STEP 6

Calculate the value of $x$ .
$x =46$

STEP 7

Now that we have the value of $x$ , we can substitute it into the equation for the measure of $\angle2$ to find its measure.
$\mathrm{m} \angle2 = (3x -17)^\circ$ $\mathrm{m} \angle2 = (3 \cdot46 -17)^\circ$

STEP 8

Calculate the measure of $\angle2$ .
$\mathrm{m} \angle2 = (138 -17)^\circ$ $\mathrm{m} \angle2 =121^\circ$ The measure of $\angle2$ is $121^\circ$ .

Was this helpful?

QuestionFind the measure of $\angle 2$ given that $\mathrm{m} \angle 1=(2 x+29)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-17)^{\circ}$ , where they are vertical angles.

Studdy Solution

STEP 1

Assumptions1. $\angle1$ and $\angle$ are vertical angles. . The measure of $\angle1$ is given by $(x+29)^\circ$ .
3. The measure of $\angle$ is given by $(3x-17)^\circ$ .
4. Vertical angles are equal in measure.

STEP 2

We know that vertical angles are equal, so we can set the measures of $\angle1$ and $\angle2$ equal to each other and solve for $x$ .
$(2x+29)^\circ = (x-17)^\circ$

STEP 3

First, we can get rid of the degree symbol since it's the same on both sides.
$2x+29 =3x-17$

STEP 4

Next, we can rearrange the equation to isolate $x$ on one side. We can do this by subtracting $2x$ from both sides.
$29 = x -17$

STEP 5

Then, we add $17$ to both sides to solve for $x$ .
$x =29 +17$

STEP 6

Calculate the value of $x$ .
$x =46$

STEP 7

Now that we have the value of $x$ , we can substitute it into the equation for the measure of $\angle2$ to find its measure.
$\mathrm{m} \angle2 = (3x -17)^\circ$ $\mathrm{m} \angle2 = (3 \cdot46 -17)^\circ$

STEP 8

Calculate the measure of $\angle2$ .
$\mathrm{m} \angle2 = (138 -17)^\circ$ $\mathrm{m} \angle2 =121^\circ$ The measure of $\angle2$ is $121^\circ$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the measure of ∠2\angle 2∠2 given that m∠1=(2x+29)∘\mathrm{m} \angle 1=(2 x+29)^{\circ}m∠1=(2x+29)∘ and m∠2=(3x−17)∘\mathrm{m} \angle 2=(3 x-17)^{\circ}m∠2=(3x−17)∘, where they are vertical angles.

Studdy Solution

STEP 1

Assumptions1. ∠1\angle1∠1 and ∠\angle∠ are vertical angles. . The measure of ∠1\angle1∠1 is given by (x+29)∘(x+29)^\circ(x+29)∘.3. The measure of ∠\angle∠ is given by (3x−17)∘(3x-17)^\circ(3x−17)∘.4. Vertical angles are equal in measure.

STEP 2

We know that vertical angles are equal, so we can set the measures of ∠1\angle1∠1 and ∠2\angle2∠2 equal to each other and solve for xxx.(2x+29)∘=(x−17)∘(2x+29)^\circ = (x-17)^\circ(2x+29)∘=(x−17)∘

STEP 3

First, we can get rid of the degree symbol since it's the same on both sides.2x+29=3x−172x+29 =3x-172x+29=3x−17

STEP 4

Next, we can rearrange the equation to isolate xxx on one side. We can do this by subtracting 2x2x2x from both sides.29=x−1729 = x -1729=x−17

STEP 5

Then, we add 171717 to both sides to solve for xxx.x=29+17x =29 +17x=29+17

STEP 6

Calculate the value of xxx.x=46x =46x=46

STEP 7

Now that we have the value of xxx, we can substitute it into the equation for the measure of ∠2\angle2∠2 to find its measure.m∠2=(3x−17)∘\mathrm{m} \angle2 = (3x -17)^\circm∠2=(3x−17)∘m∠2=(3⋅46−17)∘\mathrm{m} \angle2 = (3 \cdot46 -17)^\circm∠2=(3⋅46−17)∘

STEP 8

Calculate the measure of ∠2\angle2∠2.m∠2=(138−17)∘\mathrm{m} \angle2 = (138 -17)^\circm∠2=(138−17)∘m∠2=121∘\mathrm{m} \angle2 =121^\circm∠2=121∘The measure of ∠2\angle2∠2 is 121∘121^\circ121∘.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the measure of $\angle 2$ given that $\mathrm{m} \angle 1=(2 x+29)^{\circ}$ and $\mathrm{m} \angle 2=(3 x-17)^{\circ}$ , where they are vertical angles.

Assumptions1. $\angle1$ and $\angle$ are vertical angles. . The measure of $\angle1$ is given by $(x+29)^\circ$ .
3. The measure of $\angle$ is given by $(3x-17)^\circ$ .
4. Vertical angles are equal in measure.

We know that vertical angles are equal, so we can set the measures of $\angle1$ and $\angle2$ equal to each other and solve for $x$ .
$(2x+29)^\circ = (x-17)^\circ$

First, we can get rid of the degree symbol since it's the same on both sides.
$2x+29 =3x-17$

Next, we can rearrange the equation to isolate $x$ on one side. We can do this by subtracting $2x$ from both sides.
$29 = x -17$

Then, we add $17$ to both sides to solve for $x$ .
$x =29 +17$

Calculate the value of $x$ .
$x =46$

Now that we have the value of $x$ , we can substitute it into the equation for the measure of $\angle2$ to find its measure.
$\mathrm{m} \angle2 = (3x -17)^\circ$ $\mathrm{m} \angle2 = (3 \cdot46 -17)^\circ$

Calculate the measure of $\angle2$ .
$\mathrm{m} \angle2 = (138 -17)^\circ$ $\mathrm{m} \angle2 =121^\circ$ The measure of $\angle2$ is $121^\circ$ .