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
The image shows two parallel lines, AB and CD, intersected by a transversal line EF. We need to find the values of x, y, and z using properties of parallel lines. Step 1: Find y. The angle 74^ and angle y are adjacent angles on the straight line AB. Angles on a straight line sum to 180^. 74^ + y = 180^ y = 180^ - 74^ y = 106^ Reason: Angles on a straight line (linear pair). Step 2: Find x. The angle 74^ and angle x are alternate interior angles. Since lines AB and CD are parallel, alternate interior angles are equal. x = 74^ Reason: Alternate interior angles are equal. Step 3: Find z. Angle y and angle z are alternate interior angles. Since lines AB and CD are parallel, alternate interior angles are equal. z = y Since we found y = 106^: z = 106^ Reason: Alternate interior angles are equal. Alternatively for z: The angle 74^ and angle z are consecutive interior angles (also known as same-side interior angles). Consecutive interior angles sum to 180^. 74^ + z = 180^ z = 180^ - 74^ z = 106^ Reason: Consecutive interior angles are supplementary. The values are: x = 74^ y = 106^ z = 106^ Drop the next question 📸