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Answer :
Sure! Let's go step by step to solve the problem and find the value of [tex]\( x \)[/tex].
1. Identify the Given Information:
- The measure of angle 1 is [tex]\( 110^\circ \)[/tex].
- The measure of angle 3 is given as [tex]\( (2x + 10)^\circ \)[/tex].
2. Understanding the Relationship Between the Angles:
- If these angles are supplementary (which means they add up to [tex]\( 180^\circ \)[/tex]), then we can use this relationship to set up an equation.
3. Set Up the Equation:
- Since angle 1 and angle 3 are supplementary, their sum is [tex]\( 180^\circ \)[/tex]:
[tex]\[
110^\circ + (2x + 10)^\circ = 180^\circ
\][/tex]
4. Solve the Equation for [tex]\( x \)[/tex]:
- First, simplify the equation:
[tex]\[
110 + 2x + 10 = 180
\][/tex]
- Combine like terms:
[tex]\[
120 + 2x = 180
\][/tex]
- Subtract 120 from both sides:
[tex]\[
2x = 60
\][/tex]
- Divide by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 30
\][/tex]
5. Conclusion:
- The value of [tex]\( x \)[/tex] is 30. Let's choose the correct answer from the options given:
- 50
- 55
- 60
- 100
- None of these options matches 30, meaning the given options do not include our calculated value.
Thus, [tex]\( x = 30 \)[/tex]. Since this value isn't listed as an option, it seems there may be a typo or error in the options provided.
1. Identify the Given Information:
- The measure of angle 1 is [tex]\( 110^\circ \)[/tex].
- The measure of angle 3 is given as [tex]\( (2x + 10)^\circ \)[/tex].
2. Understanding the Relationship Between the Angles:
- If these angles are supplementary (which means they add up to [tex]\( 180^\circ \)[/tex]), then we can use this relationship to set up an equation.
3. Set Up the Equation:
- Since angle 1 and angle 3 are supplementary, their sum is [tex]\( 180^\circ \)[/tex]:
[tex]\[
110^\circ + (2x + 10)^\circ = 180^\circ
\][/tex]
4. Solve the Equation for [tex]\( x \)[/tex]:
- First, simplify the equation:
[tex]\[
110 + 2x + 10 = 180
\][/tex]
- Combine like terms:
[tex]\[
120 + 2x = 180
\][/tex]
- Subtract 120 from both sides:
[tex]\[
2x = 60
\][/tex]
- Divide by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 30
\][/tex]
5. Conclusion:
- The value of [tex]\( x \)[/tex] is 30. Let's choose the correct answer from the options given:
- 50
- 55
- 60
- 100
- None of these options matches 30, meaning the given options do not include our calculated value.
Thus, [tex]\( x = 30 \)[/tex]. Since this value isn't listed as an option, it seems there may be a typo or error in the options provided.
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