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Find the value of the unknown alphabets. Also give reasons.

To solve for the unknown angles in the given diagrams, let's analyze each one:

### (a)
The diagram shows two intersecting lines forming four angles. One of the angles is marked as \(95^\circ\).

1. **Unknown Angle \(x\):**

   Since the angles opposite each other are equal (vertical angles):

   \[
   x = 95^\circ
   \]

### (b)
The diagram shows two parallel lines intersected by a transversal creating alternate interior angles.

1. **Unknown Angle \(y\):**

   Given one angle is \(82^\circ\), the alternate interior angle \(y\) is equal to this:

   \[
   y = 82^\circ
   \]

### (c)
The diagram shows a triangle with one angle marked \(55^\circ\) and another angle marked \(x\).

1. **Unknown Angle \(x\):**

   The sum of the interior angles of a triangle is \(180^\circ\). Therefore:

   \[
   55^\circ + 55^\circ + x = 180^\circ
   \]

   \[
   110^\circ + x = 180^\circ
   \]

   \[
   x = 70^\circ
   \]

### (d)
The diagram shows a quadrilateral with three known angles \(D\), \(A\), and \(B\) with \(95^\circ\) each, and the fourth angle is \(x\).

1. **Unknown Angle \(x\):**

   The sum of the interior angles of a quadrilateral is \(360^\circ\). Therefore:

   \[
   95^\circ + 95^\circ + 95^\circ + x = 360^\circ
   \]

   \[
   285^\circ + x = 360^\circ
   \]

   \[
   x = 75^\circ
   \]

### (e)
The diagram shows parallel lines intersected by transversals creating angles marked as \(3x\) and \(2x\).

1. **Unknown Angle \(x\):**

   Since these are consecutive interior angles, they sum to \(180^\circ\):

   \[
   3x + 2x = 180^\circ
   \]

   \[
   5x = 180^\circ
   \]

   \[
   x = 36^\circ
   \]

### (f)
The diagram shows two intersecting lines forming four angles with one marked as \(60^\circ\).

1. **Unknown Angle \(x\):**

   Since the angles opposite each other are equal (vertical angles):

   \[
   x = 60^\circ
   \]

These are the values of the unknown angles in the diagrams along with their reasons.

If you want more details or have any questions, feel free to ask. Here are some related questions that expand on this information:

1. What are alternate interior angles and how are they determined?
2. How do you determine the sum of interior angles in polygons other than triangles and quadrilaterals?
3. What is the significance of vertical angles and why are they always equal?
4. How do you solve for unknown angles when two parallel lines are intersected by multiple transversals?
5. What properties of triangles can be used to determine unknown angles or sides?
6. How do you determine the angles formed when multiple lines intersect at a single point?
7. What are the properties of supplementary angles and how are they used in solving angle problems?
8. How can the exterior angles of a polygon be used to determine unknown interior angles?

### Tip:
When dealing with intersecting lines and parallel lines cut by a transversal, always look for vertical angles, alternate interior angles, and corresponding angles as they are equal and can help solve for unknown angles easily.

Discover how to find the unknown angles in geometry diagrams with detailed explanations and step-by-step solutions. This problem covers key geometric concepts such as angle properties, triangle properties, and polygon properties. Suitable for students in Grades 7-9.

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