QuestionFind $m \angle D O T$ given $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O T$ , $m \angle 1=6x+41$ , $m \angle 2=9x-1$ .

Studdy Solution

STEP 1

Assumptions1. $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ . $m \angle1=6 x+41$
3. $m \angle=9 x-1$

STEP 2

Since $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ , we know that $m \angle1 = m \angle2$ . So we can set the two expressions for $m \angle1$ and $m \angle2$ equal to each other and solve for $x$ .
$6x +41 =9x -1$

STEP 3

To solve for $x$ , we first move all terms involving $x$ to one side of the equation and the constants to the other side.
$9x -6x =41 +1$

STEP 4

implify the equation.
$3x =42$

STEP 5

Divide both sides of the equation by3 to solve for $x$ .
$x =42 /3$

STEP 6

Calculate the value of $x$ .
$x =42 /3 =14$

STEP 7

Now that we have the value of $x$ , we can substitute it back into the expression for $m \angle1$ or $m \angle2$ to find the measure of each angle.
$m \angle1 =6x +41$

STEP 8

Substitute $x =14$ into the equation.
$m \angle1 =6(14) +41$

STEP 9

Calculate the value of $m \angle$ .
$m \angle =6(14) +41 =84 +41 =125$

STEP 10

Since $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ , the measure of $\angle D O$ is twice the measure of $m \angle$ .
$m \angle D O =2 \times m \angle$

STEP 11

Substitute $m \angle =125$ into the equation.
$m \angle D O = \times125$

STEP 12

Calculate the measure of $\angle D O$ .
$m \angle D O =2 \times125 =250$ The measure of $\angle D O$ is250 degrees.

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QuestionFind $m \angle D O T$ given $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O T$ , $m \angle 1=6x+41$ , $m \angle 2=9x-1$ .

Studdy Solution

STEP 1

Assumptions1. $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ . $m \angle1=6 x+41$
3. $m \angle=9 x-1$

STEP 2

Since $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ , we know that $m \angle1 = m \angle2$ . So we can set the two expressions for $m \angle1$ and $m \angle2$ equal to each other and solve for $x$ .
$6x +41 =9x -1$

STEP 3

To solve for $x$ , we first move all terms involving $x$ to one side of the equation and the constants to the other side.
$9x -6x =41 +1$

STEP 4

implify the equation.
$3x =42$

STEP 5

Divide both sides of the equation by3 to solve for $x$ .
$x =42 /3$

STEP 6

Calculate the value of $x$ .
$x =42 /3 =14$

STEP 7

Now that we have the value of $x$ , we can substitute it back into the expression for $m \angle1$ or $m \angle2$ to find the measure of each angle.
$m \angle1 =6x +41$

STEP 8

Substitute $x =14$ into the equation.
$m \angle1 =6(14) +41$

STEP 9

Calculate the value of $m \angle$ .
$m \angle =6(14) +41 =84 +41 =125$

STEP 10

Since $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ , the measure of $\angle D O$ is twice the measure of $m \angle$ .
$m \angle D O =2 \times m \angle$

STEP 11

Substitute $m \angle =125$ into the equation.
$m \angle D O = \times125$

STEP 12

Calculate the measure of $\angle D O$ .
$m \angle D O =2 \times125 =250$ The measure of $\angle D O$ is250 degrees.

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QuestionFind m∠DOTm \angle D O Tm∠DOT given OGundefined\overrightarrow{\mathrm{OG}}OG bisects ∠DOT\angle D O T∠DOT, m∠1=6x+41m \angle 1=6x+41m∠1=6x+41, m∠2=9x−1m \angle 2=9x-1m∠2=9x−1.

Studdy Solution

STEP 1

Assumptions1. OGundefined\overrightarrow{\mathrm{OG}}OG bisects ∠DO\angle D O∠DO . m∠1=6x+41m \angle1=6 x+41m∠1=6x+413. m∠=9x−1m \angle=9 x-1m∠=9x−1

STEP 2

Since OGundefined\overrightarrow{\mathrm{OG}}OG bisects ∠DO\angle D O∠DO, we know that m∠1=m∠2m \angle1 = m \angle2m∠1=m∠2. So we can set the two expressions for m∠1m \angle1m∠1 and m∠2m \angle2m∠2 equal to each other and solve for xxx.6x+41=9x−16x +41 =9x -16x+41=9x−1

STEP 3

To solve for xxx, we first move all terms involving xxx to one side of the equation and the constants to the other side.9x−6x=41+19x -6x =41 +19x−6x=41+1

STEP 4

implify the equation.3x=423x =423x=42

STEP 5

Divide both sides of the equation by3 to solve for xxx.x=42/3x =42 /3x=42/3

STEP 6

Calculate the value of xxx.x=42/3=14x =42 /3 =14x=42/3=14

STEP 7

Now that we have the value of xxx, we can substitute it back into the expression for m∠1m \angle1m∠1 or m∠2m \angle2m∠2 to find the measure of each angle.m∠1=6x+41m \angle1 =6x +41m∠1=6x+41

STEP 8

Substitute x=14x =14x=14 into the equation.m∠1=6(14)+41m \angle1 =6(14) +41m∠1=6(14)+41

STEP 9

Calculate the value of m∠m \anglem∠.m∠=6(14)+41=84+41=125m \angle =6(14) +41 =84 +41 =125m∠=6(14)+41=84+41=125

STEP 10

Since OGundefined\overrightarrow{\mathrm{OG}}OG bisects ∠DO\angle D O∠DO, the measure of ∠DO\angle D O∠DO is twice the measure of m∠m \anglem∠.m∠DO=2×m∠m \angle D O =2 \times m \anglem∠DO=2×m∠

STEP 11

Substitute m∠=125m \angle =125m∠=125 into the equation.m∠DO=×125m \angle D O = \times125m∠DO=×125

STEP 12

Calculate the measure of ∠DO\angle D O∠DO.m∠DO=2×125=250m \angle D O =2 \times125 =250m∠DO=2×125=250The measure of ∠DO\angle D O∠DO is250 degrees.

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QuestionFind $m \angle D O T$ given $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O T$ , $m \angle 1=6x+41$ , $m \angle 2=9x-1$ .

Assumptions1. $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ . $m \angle1=6 x+41$
3. $m \angle=9 x-1$

Since $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ , we know that $m \angle1 = m \angle2$ . So we can set the two expressions for $m \angle1$ and $m \angle2$ equal to each other and solve for $x$ .
$6x +41 =9x -1$

To solve for $x$ , we first move all terms involving $x$ to one side of the equation and the constants to the other side.
$9x -6x =41 +1$

implify the equation.
$3x =42$

Divide both sides of the equation by3 to solve for $x$ .
$x =42 /3$

Calculate the value of $x$ .
$x =42 /3 =14$

Now that we have the value of $x$ , we can substitute it back into the expression for $m \angle1$ or $m \angle2$ to find the measure of each angle.
$m \angle1 =6x +41$

Substitute $x =14$ into the equation.
$m \angle1 =6(14) +41$

Calculate the value of $m \angle$ .
$m \angle =6(14) +41 =84 +41 =125$

Since $\overrightarrow{\mathrm{OG}}$ bisects $\angle D O$ , the measure of $\angle D O$ is twice the measure of $m \angle$ .
$m \angle D O =2 \times m \angle$

Substitute $m \angle =125$ into the equation.
$m \angle D O = \times125$

Calculate the measure of $\angle D O$ .
$m \angle D O =2 \times125 =250$ The measure of $\angle D O$ is250 degrees.