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work out the size of angle k. Give your answering degrees

To find the size of angle \( k \), let's analyze the given diagram and apply the properties of angles formed by intersecting lines.

1. Identify the relationships between the angles. We know that:
   - Vertical angles (opposite angles) are equal.
   - Angles on a straight line sum up to \( 180^\circ \).

2. Notice that the angles labeled \( 78^\circ \) and \( 102^\circ \) are on a straight line, so:
   \[
   78^\circ + 102^\circ = 180^\circ
   \]

3. The angles labeled \( 86^\circ \) and \( k \) are also on a straight line, so:
   \[
   86^\circ + k = 180^\circ
   \]

4. Solving for \( k \):
   \[
   k = 180^\circ - 86^\circ = 94^\circ
   \]

Therefore, the size of angle \( k \) is \( 94^\circ \).

Would you like more details or have any questions? Here are 5 additional questions you might find interesting:

1. How do you find the value of an unknown angle using complementary angles?
2. What are the properties of alternate interior angles?
3. How can you determine the sum of the interior angles of a polygon?
4. What are corresponding angles and how are they used in parallel line problems?
5. Can you explain the angle sum property of a triangle?

**Tip:** When solving problems involving intersecting lines, always look for relationships such as vertical angles, supplementary angles, and corresponding angles to find unknown values efficiently.

Learn how to determine the size of angle k in a geometric diagram using properties of angles formed by intersecting lines. This detailed explanation covers concepts such as vertical angles, the angle sum property of a straight line, and solving equations involving angles. Suitable for students in Grades 7-9.

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