QuestionFind $x$ given that $m \angle BJK = 146 + 2x$ , $m \angle IJK = 172^\circ$ , and $m \angle IJB = 2x + 26$ .

Studdy Solution

STEP 1

Assumptions1. The measure of angle BJK is given by $146 +x$ . . The measure of angle IJK is $172^{\circ}$ .
3. The measure of angle IJB is given by $x +26$ .
4. The angles are in a straight line, so they add up to $180^{\circ}$ .

STEP 2

We can use the fact that the angles on a straight line add up to $180^{\circ}$ to write an equation. The sum of the measures of angle BJK and angle IJB is equal to the measure of angle IJK.
$m \angle B J K + m \angle I J B = m \angle I J K$

STEP 3

Substitute the given expressions for the measures of the angles into the equation.
$(146+2x) + (2x+26) =172$

STEP 4

implify the equation by combining like terms.
$4x +172 =172$

STEP 5

Subtract172 from both sides of the equation to isolate the term with $x$ .
$4x =0$

STEP 6

Divide both sides of the equation by4 to solve for $x$ .
$x =0 /4$

STEP 7

Calculate the value of $x$ .
$x =0$ So, $x =0$ .

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QuestionFind $x$ given that $m \angle BJK = 146 + 2x$ , $m \angle IJK = 172^\circ$ , and $m \angle IJB = 2x + 26$ .

Studdy Solution

STEP 1

Assumptions1. The measure of angle BJK is given by $146 +x$ . . The measure of angle IJK is $172^{\circ}$ .
3. The measure of angle IJB is given by $x +26$ .
4. The angles are in a straight line, so they add up to $180^{\circ}$ .

STEP 2

We can use the fact that the angles on a straight line add up to $180^{\circ}$ to write an equation. The sum of the measures of angle BJK and angle IJB is equal to the measure of angle IJK.
$m \angle B J K + m \angle I J B = m \angle I J K$

STEP 3

Substitute the given expressions for the measures of the angles into the equation.
$(146+2x) + (2x+26) =172$

STEP 4

implify the equation by combining like terms.
$4x +172 =172$

STEP 5

Subtract172 from both sides of the equation to isolate the term with $x$ .
$4x =0$

STEP 6

Divide both sides of the equation by4 to solve for $x$ .
$x =0 /4$

STEP 7

Calculate the value of $x$ .
$x =0$ So, $x =0$ .

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QuestionFind xxx given that m∠BJK=146+2xm \angle BJK = 146 + 2xm∠BJK=146+2x, m∠IJK=172∘m \angle IJK = 172^\circm∠IJK=172∘, and m∠IJB=2x+26m \angle IJB = 2x + 26m∠IJB=2x+26.

Studdy Solution

STEP 1

Assumptions1. The measure of angle BJK is given by 146+x146 +x146+x. . The measure of angle IJK is 172∘172^{\circ}172∘.3. The measure of angle IJB is given by x+26x +26x+26.4. The angles are in a straight line, so they add up to 180∘180^{\circ}180∘.

STEP 2

We can use the fact that the angles on a straight line add up to 180∘180^{\circ}180∘ to write an equation. The sum of the measures of angle BJK and angle IJB is equal to the measure of angle IJK.m∠BJK+m∠IJB=m∠IJKm \angle B J K + m \angle I J B = m \angle I J Km∠BJK+m∠IJB=m∠IJK

STEP 3

Substitute the given expressions for the measures of the angles into the equation.(146+2x)+(2x+26)=172(146+2x) + (2x+26) =172(146+2x)+(2x+26)=172

STEP 4

implify the equation by combining like terms.4x+172=1724x +172 =1724x+172=172

STEP 5

Subtract172 from both sides of the equation to isolate the term with xxx.4x=04x =04x=0

STEP 6

Divide both sides of the equation by4 to solve for xxx.x=0/4x =0 /4x=0/4

STEP 7

Calculate the value of xxx.x=0x =0x=0So, x=0x =0x=0.

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QuestionFind $x$ given that $m \angle BJK = 146 + 2x$ , $m \angle IJK = 172^\circ$ , and $m \angle IJB = 2x + 26$ .

Assumptions1. The measure of angle BJK is given by $146 +x$ . . The measure of angle IJK is $172^{\circ}$ .
3. The measure of angle IJB is given by $x +26$ .
4. The angles are in a straight line, so they add up to $180^{\circ}$ .

We can use the fact that the angles on a straight line add up to $180^{\circ}$ to write an equation. The sum of the measures of angle BJK and angle IJB is equal to the measure of angle IJK.
$m \angle B J K + m \angle I J B = m \angle I J K$

Substitute the given expressions for the measures of the angles into the equation.
$(146+2x) + (2x+26) =172$

implify the equation by combining like terms.
$4x +172 =172$

Subtract172 from both sides of the equation to isolate the term with $x$ .
$4x =0$

Divide both sides of the equation by4 to solve for $x$ .
$x =0 /4$

Calculate the value of $x$ .
$x =0$ So, $x =0$ .