**Parallel Lines and Angles - Educational Explanation****Question:** What value of \( x \) would prove \( a \parallel b \)?**Diagram Description:**- There are two horizontal lines labeled as \( a \) and \( b \).- A transversal intersects lines \( a \) and \( b \).- The angle formed between the transversal and line \( a \) is expressed as \( 12x + 3 \).- The angle formed between the transversal and line \( b \) is expressed as \( 21x - 51 \).**Options:**a. \( x = 6.9 \) b. \( x = 6 \) c. \( x = 12 \) d. \( x = 4.2 \) For the lines \( a \) and \( b \) to be parallel, the corresponding angles need to be equal. Therefore, set the expressions equal to each other and solve for \( x \):\[ 12x + 3 = 21x - 51 \]Subtract \( 12x \) from both sides:\[ 3 = 9x - 51 \]Add 51 to both sides:\[ 54 = 9x \]Divide by 9:\[ x = 6 \]Therefore, the correct value of \( x \) that proves \( a \parallel b \) is found in option b:**Answer:** \( x = 6 \)

Name: **Parallel Lines and Angles - Educational Explanation****Question:**
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: **Parallel Lines and Angles - Educational Explanation****Question:** What value of \( x \) would prove \( a \parallel b \)?**Diagram Description:**- There are two horizontal lines labeled as \( a \) and \( b \).- A transversal intersects lines \( a