Question
angles of a triangle are y , ( y + 12) , (y + 18) find the value of y
Answers
GPT-4o
In any triangle, the sum of the interior angles is always \( 180^\circ \). Given the angles of the triangle as \( y \), \( y + 12 \), and \( y + 18 \), we can set up and solve the following equation:
\[ y + (y + 12) + (y + 18) = 180 \]
Combine like terms:
\[ y + y + 12 + y + 18 = 180 \]
\[ 3y + 30 = 180 \]
Subtract 30 from both sides to isolate the term with \( y \):
\[ 3y = 150 \]
Divide both sides by 3 to solve for \( y \):
\[ y = 50 \]
So, the value of \( y \) is \( 50 \).
To ensure the solution is correct, we can verify by calculating the angles and confirming that their sum is \( 180^\circ \):
\[ y = 50 \]
\[ y + 12 = 50 + 12 = 62 \]
\[ y + 18 = 50 + 18 = 68 \]
Now, sum the angles:
\[ 50 + 62 + 68 = 180 \]
The calculation is correct, confirming that the value of \( y \) is indeed \( 50 \).
\[ y + (y + 12) + (y + 18) = 180 \]
Combine like terms:
\[ y + y + 12 + y + 18 = 180 \]
\[ 3y + 30 = 180 \]
Subtract 30 from both sides to isolate the term with \( y \):
\[ 3y = 150 \]
Divide both sides by 3 to solve for \( y \):
\[ y = 50 \]
So, the value of \( y \) is \( 50 \).
To ensure the solution is correct, we can verify by calculating the angles and confirming that their sum is \( 180^\circ \):
\[ y = 50 \]
\[ y + 12 = 50 + 12 = 62 \]
\[ y + 18 = 50 + 18 = 68 \]
Now, sum the angles:
\[ 50 + 62 + 68 = 180 \]
The calculation is correct, confirming that the value of \( y \) is indeed \( 50 \).