A pie chart shows the distribution of animals on a farm. Goats are represented by 120 degrees, sheep by 90 degrees, and chickens by 60 degrees. If there were 15 more sheep than goats, how many more ca

The angle representing cattle is $\boxed{\text{90 degrees}}$.

b) The question states there were 15 more sheep than goats, but based on the degrees, goats ($120^\circ$) are more than sheep ($90^\circ$). We will interpret "15 more sheep than goat" as the absolute difference in the number of animals corresponding to the difference in their angles.

Since $30^\circ$ corresponds to 15 animals,

Cattle: $90^\circ \times 0.5 \text{ animals/degree} = 45 \text{ animals}$
Chicken: $60^\circ \times 0.5 \text{ animals/degree} = 30 \text{ animals}$

There were $\boxed{\text{15 more cattle than chicken}}$.

2. Straight Line Equation
The equation of a straight line is $2y = x + 11$. We need to find the value of $x$ when $y = 2$.

The value of $x$ when $y=2$ is $\boxed{-7}$.

3. Ratios
Given $a:b = 4:3$ and $b:c = 4:5$. We need to find the ratio $a:c$.

The least common multiple is 12.

For $a:b = 4:3$, multiply both parts by 4:

For $b:c = 4:5$, multiply both parts by 3:

Now we have $a:b:c = 16:12:15$.
Therefore, $a:c = 16:15$.
The ratio $a:c$ is $\boxed{16:15}$.

4. Percentage Loss
Juan sold a jacket for 1800 and made a 10% loss. We need to find the original cost price.

The selling price ($S$) is 1800.
A 10% loss means the selling price is $100\% - 10\% = 90\%$ of the cost price.

Juan had bought the jacket for $\boxed{\text{2000}}$.

5. Length of Wire for Fencing
The figure shows a sector of a circle with a radius of 140 m and an angle of $80^\circ$. The farm was fenced using two strands of wire.

The formula for arc length is $L = \frac{\theta}{360^\circ} \times 2\pi r$.
Given $\theta = 80^\circ$ and $r = 140$ m.

The perimeter of the sector includes the two radii and the arc length.
Perimeter (one strand) $= 2r + L$

Total length $= 2 \times P$

The total length of wire that was used is approximately $\boxed{\text{951.0 m}}$.