Let's solve each question by calculating the missing angles based on the given information.

Solution:

(a)

The angles given are $15^\circ$ and $25^\circ$. These are two adjacent angles on a straight line, so we can calculate the third angle.

1. Straight line total angle = $180^\circ$.
2. Missing angle = $180^\circ - (15^\circ + 25^\circ) = 180^\circ - 40^\circ = 140^\circ$.

So, the missing angle is $140^\circ$.

(b)

In this triangle, there are two equal sides (indicated by the markings), making it an isosceles triangle. One angle is given as $92^\circ$.

1. Total angle sum in a triangle = $180^\circ$.
2. Sum of the other two angles = $180^\circ - 92^\circ = 88^\circ$.
3. Since it’s an isosceles triangle, each of these angles will be $88^\circ / 2 = 44^\circ$.

So, the missing angles are both $44^\circ$.

(c)

Here we have a pair of parallel lines cut by a transversal. One angle is $118^\circ$, and an adjacent angle is $38^\circ$.

1. Since $118^\circ$ and $38^\circ$ are on a straight line, they form a linear pair, confirming that $118^\circ + 38^\circ = 156^\circ$.
2. By corresponding angles, the angle opposite to $38^\circ$ is also $38^\circ$, and the angle opposite to $118^\circ$ is $118^\circ$.

(d)

In this figure, we have a pair of intersecting lines with angles of $71^\circ$ and $29^\circ$.

1. The angle opposite $71^\circ$ (vertically opposite) will also be $71^\circ$.
2. The angle opposite $29^\circ$ (vertically opposite) will also be $29^\circ$.
3. The remaining angles on each side of the intersection add up to $180^\circ$: $180^\circ - 71^\circ = 109^\circ$ and $180^\circ - 29^\circ = 151^\circ$.

So, the missing angles are $71^\circ$, $29^\circ$, $109^\circ$, and $151^\circ$.

Would you like detailed steps for each calculation, or have any questions?

Here are five questions to further explore this topic:

1. How do we determine if a triangle is isosceles or not?
2. What is the rule for calculating angles on a straight line?
3. How can you find the angles in a parallelogram?
4. What is the significance of vertically opposite angles in geometry?
5. How can corresponding and alternate angles help in solving problems involving parallel lines?

Tip: Remember that the sum of angles in a triangle is always $180^\circ$, a fundamental property helpful for many angle-related problems.