Certainly! Let's break down the solution step-by-step for the given problem.
### Step 1: Identify the Angle Relationship
The angles given are described as "Same Side Interior" angles. According to the properties of Same Side Interior angles, their sum is always 180 degrees.
### Step 2: Write Down the Given Information
We have two angles:
1. The first angle is [tex]\( 6x + 21 \)[/tex] degrees.
2. The second angle is 87 degrees.
### Step 3: Set Up the Equation
Since Same Side Interior angles sum to 180 degrees, we can set up the following equation:
[tex]\[
(6x + 21) + 87 = 180
\][/tex]
### Step 4: Combine Like Terms
Combine the constants (21 and 87) on the left-hand side of the equation:
[tex]\[
6x + 108 = 180
\][/tex]
### Step 5: Isolate the Variable Term
Move the constant term (108) to the right-hand side of the equation by subtracting it from both sides:
[tex]\[
6x = 180 - 108
\][/tex]
Simplify the right-hand side:
[tex]\[
6x = 72
\][/tex]
### Step 6: Solve for [tex]\( x \)[/tex]
To isolate [tex]\( x \)[/tex], divide both sides of the equation by 6:
[tex]\[
x = \frac{72}{6}
\][/tex]
Simplify the fraction:
[tex]\[
x = 12
\][/tex]
### Conclusion
The value of [tex]\( x \)[/tex] that satisfies the given equation and the properties of Same Side Interior angles is [tex]\( x = 12 \)[/tex].
