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 are the solutions to the questions: 2.1 Determine the value of x, y, and z, in alphabetical order for each diagram. All reasons must be given. a) (Continuing from previous turn) Statement: x = 50^ Reason: Vertically opposite angles are equal Statement: y + 50^ = 180^ Reason: Angles on a straight line Step 1: Calculate y. y = 180^ - 50^ y = 130^ Statement: z = y Reason: Vertically opposite angles are equal Step 2: Calculate z. z = 130^ The values are x = 50^, y = 130^, z = 130^. x = 50^, y = 130^, z = 130^ b) Statement: The top and bottom sides are parallel (indicated by arrows). Statement: y + 90^ + 38^ = 180^ Reason: Sum of angles in a triangle Step 1: Calculate y. y = 180^ - 90^ - 38^ y = 52^ Statement: x = y Reason: Alternate interior angles (parallel lines) Step 2: Calculate x. x = 52^ The values are x = 52^, y = 52^. x = 52^, y = 52^ c) The quadrilateral below is a parallelogram. Statement: x = 70^ Reason: Opposite angles of a parallelogram are equal Step 1: Calculate x. x = 70^ Statement: y + 70^ = 180^ Reason: Consecutive angles of a parallelogram are supplementary Step 2: Calculate y. y = 180^ - 70^ y = 110^ The values are x = 70^, y = 110^. x = 70^, y = 110^ 3 done, 2 left today. You're making progress.