Lesson Summary

Welcome to Civil Engineering Academy's module 1B on Survey Mathematics and Geometry. Let's start with angles, the space between two lines diverging from a common point or a vertex:

• Angles are commonly measured in degrees, with 1 degree being 1/360th of a circle.
• A circle is divided into 360 equal arcs with radii forming angles of 1 degree.
• Each degree can further be divided into 60 minutes, and each minute into 60 seconds.

Angles can also be measured in radians, where 1 radian is approximately 57.296 degrees. Different angle names include a right angle (90 degrees), a straight angle (180 degrees), an acute angle (less than 90 degrees), and an obtuse angle (more than 90 but less than 180 degrees).

• Complementary angles share a 90-degree space, while supplementary angles share a 180-degree space.
• Transversal lines can create alternate interior and exterior angles when intersecting parallel lines.

When adding or subtracting angles:

• Line up angles by degrees, minutes, and seconds.
• Handle any values exceeding 60 by subtracting 60 from the current measurement and adding 1 to the next larger unit.

For polygons:

• Right triangles have a 90-degree angle, isosceles triangles have two equal sides and angles, and equilateral triangles have all sides and angles equal.
• Sum of interior angles can be found using the formula: (n-2) * 180, where n is the number of sides.

In a circle:

• The radius is from the center to any point on the circle, and the diameter is a line passing through the center.
• A chord is a straight line connecting two points within a circle.
• Tangent lines intersect the circle at a single point, while secant lines intersect at two points.

Other circle properties include sectors, segments, concentric circles, and intersecting chords. Understanding these concepts is essential for civil engineering. That’s it for this module - see you in the next one!