This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the value of y, we use the properties of parallel lines intersected by a transversal. From the diagram, l_1 l_2, and l_3 is a transversal. Step 1: Identify the relationship between the angles involving x. The angle marked x^ is an exterior angle. The angle vertically opposite to this x^ is an interior angle on line l_1 to the left of the transversal l_3. This interior angle also measures x^. The angle marked 3x^ is an interior angle on line l_2 to the right of the transversal l_3. Since l_1 l_2, the interior angle x^ (on l_1 to the left) and the interior angle 3x^ (on l_2 to the right) are consecutive interior angles (also known as same-side interior angles). The sum of consecutive interior angles is 180^. x^ + 3x^ = 180^ Step 2: Solve for x. Combine the terms: 4x^ = 180^ Divide by 4: x^ = (180^)/(4) x^ = 45^ Step 3: Identify the relationship between x^ and y^. The angle y^ is an interior angle on line l_1 to the right of the transversal l_3. The interior angle x^ (on l_1 to the left of l_3, which is vertically opposite to the given exterior x^) and y^ form a linear pair on line l_1. The sum of angles in a linear pair is 180^. x^ + y^ = 180^ Step 4: Solve for y. Substitute the value of x^ found in Step 2 into the equation: 45^ + y^ = 180^ Subtract 45^ from both sides: y^ = 180^ - 45^ y^ = 135^ The value of y is 135. The final answer is 135. That's 2 down. 3 left today — send the next one.