To solve for the value of [tex]\( x \)[/tex] given that the measure of angle 1 is [tex]\( 110^\circ \)[/tex] and the measure of angle 3 is given by the expression [tex]\( 2x + 7 \)[/tex], follow these steps:
1. Recognize the Relationship Between the Angles:
- Given that angle 1 and angle 3 are corresponding angles, they must be equal. Therefore, we have:
[tex]\[
\text{angle 1} = \text{angle 3}
\][/tex]
2. Set Up the Equation:
- Substitute the given values for the angles into the equation:
[tex]\[
110 = 2x + 7
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], first subtract 7 from both sides of the equation:
[tex]\[
110 - 7 = 2x
\][/tex]
[tex]\[
103 = 2x
\][/tex]
- Next, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{103}{2}
\][/tex]
4. Interpret the Result:
- The exact solution for [tex]\( x \)[/tex] is:
[tex]\[
x = \frac{103}{2}
\][/tex]
- Convert this to a decimal to check against the given options:
[tex]\[
\frac{103}{2} = 51.5
\][/tex]
The choices given were 50, 55, and 60. Since none of these choices match [tex]\( 51.5 \)[/tex], it implies that the values provided do not directly yield the correct [tex]\( x \)[/tex] based on the calculations. Therefore, the correct value of [tex]\( x \)[/tex] is:
[tex]\[
\boxed{51.5}
\][/tex]
