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
Here's how to find the marked angles: Step 1: Identify parallel lines and transversals. The two horizontal lines are parallel. The slanted line that passes through t, y, s, is a transversal. The other slanted line that forms the 30^ angle is a separate transversal. Step 2: Find angle t. The angle marked 70^ and angle t are angles on a straight line (linear pair) with respect to the top parallel line and the right transversal. They are also consecutive interior angles if we consider the transversal and the top parallel line. The 70^ angle is an alternate interior angle to the angle below the top parallel line, on the left side of the transversal. The 70^ angle and angle t are supplementary angles because they form a linear pair along the transversal. t + 70^ = 180^ t = 180^ - 70^ t = 110^ Step 3: Find angles y, s, and . Since the two horizontal lines are parallel, we can use properties of parallel lines and transversals. Angle t and angle y are consecutive interior angles. Therefore, they are supplementary. t + y = 180^ 110^ + y = 180^ y = 180^ - 110^ y = 70^ Angle s and angle y are vertically opposite angles. Therefore, they are equal. s = y s = 70^ Angle and angle t are alternate exterior angles. Therefore, they are equal. = t = 110^ Alternatively, angle and angle y are angles on a straight line (linear pair). + y = 180^ + 70^ = 180^ = 180^ - 70^ = 110^ The 30^ angle is not used to find t, y, s, as it is formed by a different transversal. If it were part of the same transversal, the problem would be different. Based on the drawing, it's an angle formed by a separate line. The marked angles are: t = 110^ y = 70^ s = 70^ = 110^ Send me the next one 📸