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Answer :
To solve the problem, let's first understand what we need to do. We are given two angles, angle 1 and angle 3, and we are told that:
- The measure of angle 1 is [tex]\(110^{\circ}\)[/tex].
- The measure of angle 3 is given by the expression [tex]\((2x + 10)^{\circ}\)[/tex].
We need to find the value of [tex]\(x\)[/tex].
Since there are no additional details about how angle 1 and angle 3 are related, we'll assume they are equal for the sake of this problem, as the question implies this relationship by having us solve for [tex]\(x\)[/tex].
Here's how you can find the value of [tex]\(x\)[/tex]:
1. Set up the equation: Since we're assuming the angles are equal (because we're solving for [tex]\(x\)[/tex] as if angle 1 and angle 3 are meant to match according to the problem), we can set their measures equal to each other.
[tex]\[
110 = 2x + 10
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
- Start by isolating [tex]\(2x\)[/tex] on one side:
[tex]\[
110 - 10 = 2x
\][/tex]
[tex]\[
100 = 2x
\][/tex]
- Next, divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{100}{2}
\][/tex]
[tex]\[
x = 50
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(50\)[/tex].
- The measure of angle 1 is [tex]\(110^{\circ}\)[/tex].
- The measure of angle 3 is given by the expression [tex]\((2x + 10)^{\circ}\)[/tex].
We need to find the value of [tex]\(x\)[/tex].
Since there are no additional details about how angle 1 and angle 3 are related, we'll assume they are equal for the sake of this problem, as the question implies this relationship by having us solve for [tex]\(x\)[/tex].
Here's how you can find the value of [tex]\(x\)[/tex]:
1. Set up the equation: Since we're assuming the angles are equal (because we're solving for [tex]\(x\)[/tex] as if angle 1 and angle 3 are meant to match according to the problem), we can set their measures equal to each other.
[tex]\[
110 = 2x + 10
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
- Start by isolating [tex]\(2x\)[/tex] on one side:
[tex]\[
110 - 10 = 2x
\][/tex]
[tex]\[
100 = 2x
\][/tex]
- Next, divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{100}{2}
\][/tex]
[tex]\[
x = 50
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(50\)[/tex].
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