Using a scale of 2cm to 1 unit on both axes, draw the graph of y=2x+5 for the values of x from -3 to +4. 2. Find the size of the lettered angles. Give reasons for your answers. 3. Calculate the size of each angle of a regular Octagon.

Step 1: Prepare for graphing y = 2x + 5. To draw the graph, first create a table of values for x from -3 to 4. Substitute each x value into the equation y = 2x + 5 to find the corresponding y value. | x | 2x | +5 | y = 2x + 5 | (x, y) | |:---:|:----:|:----:|:------------:|:--------:| | -3 | -6 | +5 | -1 | (-3, -1) | | -2 | -4 | +5 | 1 | (-2, 1) | | -1 | -2 | +5 | 3 | (-1, 3) | | 0 | 0 | +5 | 5 | (0, 5) | | 1 | 2 | +5 | 7 | (1, 7) | | 2 | 4 | +5 | 9 | (2, 9) | | 3 | 6 | +5 | 11 | (3, 11) | | 4 | 8 | +5 | 13 | (4, 13) | Step 2: Plot the graph. • Draw two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical). • Mark the origin (0,0) where the axes intersect. • Apply the scale: 2 cm represents 1 unit on both axes. This means every 2 cm grid line on your graph paper will be labeled as 1, 2, 3, for positive values and -1, -2, -3, for negative values. • Plot the points from the table: (-3, -1), (-2, 1), (-1, 3), (0, 5), (1, 7), (2, 9), (3, 11), (4, 13). • Draw a straight line connecting all the plotted points. This line is the graph of y = 2x + 5. Step 3: Find the size of the lettered angles. The diagram shows two parallel lines intersected by a transversal. The given angle is 72^. • Angle b: Angles on a straight line sum to 180^. b = 180^ - 72^ = 108^ • Angle d: Vertically opposite angles are equal. d = 72^ • Angle c: Angles on a straight line sum to 180^. c = 180^ - d = 180^ - 72^ = 108^ (Alternatively, c is vertically opposite to b, so c = b = 108^) Since the lines are parallel: • Angle e: Corresponding angles are equal. e = 72^ • Angle f: Corresponding angles are equal. f = b = 108^ (Alternatively, e and f are angles on a straight line, so f = 180^ - e = 180^ - 72^ = 108^) • Angle g: Vertically opposite angles are equal. g = e = 72^ (Alternatively, g and d are corresponding angles, so g = d = 72^) • Angle h: Vertically opposite angles are equal. h = f = 108^ (Alternatively, h and c are corresponding angles, so h = c = 108^) Step 4: Calculate the size of each angle of a regular octagon. A regular octagon has n=8 sides. The formula for the sum of interior angles of a polygon is (n-2) × 180^. The sum of interior angles of an octagon is: (8-2) × 180^ = 6 × 180^ = 1080^ For a regular polygon, all interior angles are equal. So, each interior angle is the sum divided by the number of sides. Each angle = (1080^)/(8) = 135^ Send me the next one 📸