Answer :
To solve this question, we need to evaluate each option by solving the equations for [tex]\( x \)[/tex] and [tex]\( y \)[/tex]. Let's go through each choice:
Option A:
1. [tex]\( 26 + x + 43 = 90 \)[/tex]
- Combine and simplify: [tex]\( x + 69 = 90 \)[/tex]
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 90 - 69 = 21 \)[/tex]
2. [tex]\( 118 - y = 180 \)[/tex]
- Simplify and solve for [tex]\( y \)[/tex]: [tex]\( -y = 180 - 118 = 62 \)[/tex]
- Therefore, [tex]\( y = -62 \)[/tex]
Option B:
1. [tex]\( x + 43 = 90 \)[/tex]
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 90 - 43 = 47 \)[/tex]
2. [tex]\( 26 + 118 - y = 90 \)[/tex]
- Simplify: [tex]\( 144 - y = 90 \)[/tex]
- Solve for [tex]\( y \)[/tex]: [tex]\( y = 144 - 90 = 54 \)[/tex]
Option C:
1. [tex]\( 26 + x + 13 = 180 \)[/tex]
- Combine and simplify: [tex]\( x + 39 = 180 \)[/tex]
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 180 - 39 = 141 \)[/tex]
2. [tex]\( 118 - y = 90 \)[/tex]
- Simplify and solve for [tex]\( y \)[/tex]: [tex]\( -y = 90 - 118 = -28 \)[/tex]
- Therefore, [tex]\( y = 28 \)[/tex]
Option D:
1. [tex]\( 26 + x + 43 = 90 \)[/tex]
- Combine and simplify: [tex]\( x + 69 = 90 \)[/tex]
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 90 - 69 = 21 \)[/tex]
2. [tex]\( 118 - y = 90 \)[/tex]
- Simplify and solve for [tex]\( y \)[/tex]: [tex]\( -y = 90 - 118 = -28 \)[/tex]
- Therefore, [tex]\( y = 28 \)[/tex]
After evaluating all options, option D is the correct choice because it results in [tex]\( x = 21 \)[/tex] and [tex]\( y = 28 \)[/tex].
Option A:
1. [tex]\( 26 + x + 43 = 90 \)[/tex]
- Combine and simplify: [tex]\( x + 69 = 90 \)[/tex]
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 90 - 69 = 21 \)[/tex]
2. [tex]\( 118 - y = 180 \)[/tex]
- Simplify and solve for [tex]\( y \)[/tex]: [tex]\( -y = 180 - 118 = 62 \)[/tex]
- Therefore, [tex]\( y = -62 \)[/tex]
Option B:
1. [tex]\( x + 43 = 90 \)[/tex]
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 90 - 43 = 47 \)[/tex]
2. [tex]\( 26 + 118 - y = 90 \)[/tex]
- Simplify: [tex]\( 144 - y = 90 \)[/tex]
- Solve for [tex]\( y \)[/tex]: [tex]\( y = 144 - 90 = 54 \)[/tex]
Option C:
1. [tex]\( 26 + x + 13 = 180 \)[/tex]
- Combine and simplify: [tex]\( x + 39 = 180 \)[/tex]
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 180 - 39 = 141 \)[/tex]
2. [tex]\( 118 - y = 90 \)[/tex]
- Simplify and solve for [tex]\( y \)[/tex]: [tex]\( -y = 90 - 118 = -28 \)[/tex]
- Therefore, [tex]\( y = 28 \)[/tex]
Option D:
1. [tex]\( 26 + x + 43 = 90 \)[/tex]
- Combine and simplify: [tex]\( x + 69 = 90 \)[/tex]
- Solve for [tex]\( x \)[/tex]: [tex]\( x = 90 - 69 = 21 \)[/tex]
2. [tex]\( 118 - y = 90 \)[/tex]
- Simplify and solve for [tex]\( y \)[/tex]: [tex]\( -y = 90 - 118 = -28 \)[/tex]
- Therefore, [tex]\( y = 28 \)[/tex]
After evaluating all options, option D is the correct choice because it results in [tex]\( x = 21 \)[/tex] and [tex]\( y = 28 \)[/tex].
