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.

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.

• 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: $2 \text{ cm}$ represents $1 \text{ unit}$ on both axes. This means every $2 \text{ cm}$ grid line on your graph paper will be labeled as $1, 2, 3, \dots$ for positive values and $-1, -2, -3, \dots$ 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 $y = 2x + 5$.

The diagram shows two parallel lines intersected by a transversal. The given angle is $72^\circ$.

• Angle $b$: Angles on a straight line sum to $180^\circ$.

• Angle $d$: Vertically opposite angles are equal.

• Angle $c$: Angles on a straight line sum to $180^\circ$.

(Alternatively, $c$ is vertically opposite to $b$, so $c = b = 108^\circ$)

Since the lines are parallel:

• Angle $e$: Corresponding angles are equal.

• Angle $f$: Corresponding angles are equal.

(Alternatively, $e$ and $f$ are angles on a straight line, so $f = 180^\circ - e = 180^\circ - 72^\circ = 108^\circ$)

• Angle $g$: Vertically opposite angles are equal.

(Alternatively, $g$ and $d$ are corresponding angles, so $g = d = 72^\circ$)

• Angle $h$: Vertically opposite angles are equal.

(Alternatively, $h$ and $c$ are corresponding angles, so $h = c = 108^\circ$)

A regular octagon has $n=8$ sides.
The formula for the sum of interior angles of a polygon is $(n-2) \times 180^\circ$.
The sum of interior angles of an octagon is:

For a regular polygon, all interior angles are equal. So, each interior angle is the sum divided by the number of sides.