Certainly! Let's solve the problem step-by-step.
We are given a scenario where a carpenter built a wall that forms a [tex]$90^{\circ}$[/tex] angle with the floor. Additionally, the carpenter built a ramp coming out from the point where the wall meets the floor, creating two adjacent angles.
One of the angles formed between the ramp and the wall is given as [tex]$49^{\circ}$[/tex]. We need to find the measure of the other adjacent angle created by the ramp and the floor.
### Step-by-Step Solution:
1. Understand the relationship between the angles:
- The problem states that the wall and the floor form a [tex]$90^{\circ}$[/tex] angle.
- The ramp creates two adjacent angles with the wall and the floor, which together should still sum up to [tex]$90^{\circ}$[/tex].
2. Identify the given angle:
- The given angle between the ramp and the wall is [tex]$49^{\circ}$[/tex].
3. Calculate the measure of the other angle:
- Let's denote the measure of the other angle we need to find as [tex]\( x \)[/tex].
- Since the sum of the two adjacent angles must equal the total angle formed by the wall and the floor, we can set up the equation:
[tex]\[
49^{\circ} + x = 90^{\circ}
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Subtracting [tex]$49^{\circ}$[/tex] from both sides of the equation:
[tex]\[
x = 90^{\circ} - 49^{\circ}
\][/tex]
[tex]\[
x = 41^{\circ}
\][/tex]
So, the measure of the other angle created by the ramp and the floor is:
[tex]\[
\boxed{41^{\circ}}
\][/tex]
The correct answer is:
A. [tex]$41^{\circ}$[/tex]
