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To find the measure of angle \( \angle 1 \), we need to consider the triangle formed at the base of the lookout tower. From the diagram, we can see that:

- One angle is \( 36^\circ \).
- Another angle is \( 62^\circ \).
- We are asked to find \( \angle 1 \).

Since the sum of the angles in any triangle equals \( 180^\circ \), we can use this information to find \( \angle 1 \).

\[
\angle 1 = 180^\circ - (36^\circ + 62^\circ)
\]
\[
\angle 1 = 180^\circ - 98^\circ = 82^\circ
\]

So, the measure of \( \angle 1 \) is \( 82^\circ \).

Would you like more details or have any other questions?

Here are five related questions to expand on this:

1. How do we calculate the angles of a triangle in 3D structures like towers?
2. Why do the angles of a triangle always sum to \(180^\circ\)?
3. What are the properties of different types of triangles (acute, obtuse, etc.)?
4. How can trigonometry be used to find angles in more complex structures?
5. How do vertical and alternate interior angles help in such geometry problems?

**Tip:** Always check if the structure forms a right triangle, as it simplifies calculations using the Pythagorean theorem.

In this geometry problem, learn how to calculate the measure of angle 1 using the Triangle Angle Sum Theorem. The triangle has two known angles: 36° and 62°. The sum of the angles of a triangle equals 180°, making this a straightforward calculation for students in Grades 6-8.

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