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If the measure of angle 1 is [tex]110^{\circ}[/tex] and the measure of angle 3 is [tex](2x + 10)^{\circ}[/tex], what is the value of [tex]x[/tex]?

A. 50
B. 55
C. 60
D. 100

Answer :

Certainly! Let's go through a step-by-step solution for the problem:

We are given two angles:

1. The measure of angle 1 is [tex]\(110^\circ\)[/tex].
2. The measure of angle 3 is expressed as [tex]\((2x + 10)^\circ\)[/tex].

The problem doesn't specify the relationship between these angles, but given the context, we can assume that these angles might be directly compared or complementary part of an angle relationship like being equal or supplementary.

### Step-by-Step Solution:

1. Set Up the Equation:
- We assume the two angles might be equal. This is a common initial assumption in this type of angle problem. So, we set:
[tex]\[
2x + 10 = 110
\][/tex]

2. Solve for [tex]\(x\)[/tex]:
- Subtract 10 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
2x + 10 - 10 = 110 - 10
\][/tex]
[tex]\[
2x = 100
\][/tex]

- Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{100}{2}
\][/tex]
[tex]\[
x = 50
\][/tex]

So, the value of [tex]\(x\)[/tex] is [tex]\(50\)[/tex].

Therefore, the answer is [tex]\(50\)[/tex].

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