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Answer :
To find the value of [tex]\( x \)[/tex], we need to understand the relationship between angle 1 and angle 3. Given that the measure of angle 1 is [tex]\( 110^\circ \)[/tex] and the measure of angle 3 is given by the expression [tex]\( (2x + 10)^\circ \)[/tex], we need more information about how these angles are connected. However, based on the typical context you might find in questions like this, angles on a straight line sum up to [tex]\( 180^\circ \)[/tex]. Let's assume angles 1 and 3 are supplementary (meaning they add up to [tex]\( 180^\circ \)[/tex]).
Here's how you can solve it step-by-step:
1. Set up the Equation:
- Since angles on a straight line add up to [tex]\( 180^\circ \)[/tex], we can write the equation:
[tex]\[
110 + (2x + 10) = 180
\][/tex]
2. Simplify the Equation:
- First, combine the constant terms on the left side:
[tex]\[
120 + 2x = 180
\][/tex]
- Next, subtract 120 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x = 60
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 30
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 30 \)[/tex], which matches none of the provided options, indicating that there might be a mistake in the initial coding output or an inconsistency with the provided answer choices. Based on typical expectations, options may have been misconstrued.
Here's how you can solve it step-by-step:
1. Set up the Equation:
- Since angles on a straight line add up to [tex]\( 180^\circ \)[/tex], we can write the equation:
[tex]\[
110 + (2x + 10) = 180
\][/tex]
2. Simplify the Equation:
- First, combine the constant terms on the left side:
[tex]\[
120 + 2x = 180
\][/tex]
- Next, subtract 120 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x = 60
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 30
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 30 \)[/tex], which matches none of the provided options, indicating that there might be a mistake in the initial coding output or an inconsistency with the provided answer choices. Based on typical expectations, options may have been misconstrued.
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