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To find the value of angle \( k \) in the given diagram, we can use geometric principles involving triangles and angles around points. Here is the step-by-step process:

### Step 1: Interior Angles in the Triangle
The sum of interior angles in any triangle is \( 180^\circ \). In this case, the triangle is formed by the angles \( 62^\circ \), \( 79^\circ \), and \( k \). Therefore, we can set up the equation:

\[
62^\circ + 79^\circ + k = 180^\circ
\]

### Step 2: Solve for \( k \)

\[
141^\circ + k = 180^\circ
\]

\[
k = 180^\circ - 141^\circ
\]

\[
k = 39^\circ
\]

Thus, the size of the angle marked \( k \) is \( 39^\circ \).

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Would you like more details or have further questions? Here are five questions to expand on this:

1. What is the formula for finding the sum of the interior angles of any polygon?
2. How do we find the exterior angle of a triangle?
3. Can the angles of any polygon sum to more than \( 360^\circ \)?
4. Why do the angles around a point always sum to \( 360^\circ \)?
5. How would the angle \( k \) change if the triangle were isosceles?

### Tip:
When solving problems involving polygons, always remember the relationship between the sum of interior angles and the number of sides! For an \( n \)-sided polygon, the sum of its interior angles is \( 180(n-2) \) degrees.

Work out the size of the angle marked k in a triangle placed on top of an irregular pentagon, given other angles.

Solve for the unknown angle in a triangle using the interior angle sum property, with angles provided as 62°, 79°, and k. Learn how to apply geometric principles to solve for k using the equation 62° + 79° + k = 180°. Suitable for Grades 8-10.

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