# Master Geometry Angles with Theorems and Problems - Part 1: Essential Concepts for Solving Angle Problems

In geometry, an angle is formed when two lines or rays meet at a common point. The measure of an angle is typically expressed in degrees, although other units such as radians may also be used.
Here are some important concepts related to angles in geometry:

1. Acute angle: An angle that measures less than 90 degrees.

2. Right angle: An angle that measures exactly 90 degrees.

3. Obtuse angle: An angle that measures between 90 and 180 degrees.

4. Straight angle: An angle that measures exactly 180 degrees.

5. Reflex angle: An angle that measures between 180 and 360 degrees.

6. Complementary angles: Two angles that add up to 90 degrees.

7. Supplementary angles: Two angles that add up to 180 degrees.

8. Vertical angles: A pair of opposite angles formed by the intersection of two lines. Vertical angles are equal in measure.

9. Adjacent angles: Two angles that share a common vertex and a common side. The sum of adjacent angles is equal to the measure of the larger angle formed by their non-common sides.

10. Congruent angles: Two angles that have the same measure.

Understanding these concepts is essential in solving geometry problems involving angles.

Index

Euclid's Elements Book I, 23 Definitions. One-page visual illustration. Angles and more.
Euclid's Elements Book. Index.

Points, Theorems and Problems - Index.
Vertex.

Meanings and syntactic of 'ANGLE'.
Created using Wordflex Touch Dictionary for iPad in association with Oxford University Press.

Obtuse Angle. Theorems and Problems.

Isogonal Lines.
Theorems and Problems.

Billiards and Geometry - Index
Angles of Incidence and Reflection.

Incenter. Index.
Angle bisectors.

Excenter. Index.
Interior and Exterior Angle bisectors.

Inca Stone of Twelve Angles, Cuzco. Tunnel effect.

Morley's Triangle & Center: Trisection of angles.

Blanchet Theorem. Altitude, Angle Bisector.

Isogonic-Jacobi Theorem: Using TracenPoche Dynamic Geometry Software

Mascheroni Construction with compass alone. Midpoint of a segment. Equal angles.

Interactive Simson Line. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Vertical angles.

Triangle: Incircle, Perpendicular, Angle Bisector. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.

Geometry Problem 1520 and a Thematic Poem.
Discovering Distances in a Rectangle with an Exterior Point: A Geometry Challenge.

Geometry Problem 1518 and a Thematic Poem.
Boost Your Geometry Skills: Solve for the Number of Sides in an Equiangular Polygon with an Interior Point and Bisected Angle.

Geometry Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School.

Geometry Problem 1507.
Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School.

Geometry Problem 1506.
Parallel Rays, Angles, Corresponding, Alternate.

Geometry Problem 1505.
Parallel Rays, Angles, and Bisector, Corresponding, Alternate, Conjugate.

Geometry Problem 1504.
Squares, Equilateral Triangle, Parallel, Angle.

Geometry Problem 1491.
Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement.

Geometry Problem 1490.
Triangle, Cevian, Incircle, Tangent, Measurement.

Geometry Problem 1442.
Triangle, Altitudes, Orthocenter, Perpendicular, Congruent Angles, Similarity, Measurement, Art, Poster, Typography, iPad Apps.

Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping.

Geometry Problem 1429.
Triangle, Median, 15-30 degree, Angle, Congruence.

Geometry Problem 1423.
Triangle, Area, Three Equal Angles, Circumradius, Measurement.

Geometry Problem 1418.
Triangle, Circumcircle, Incenter, Side, Sum of Segments, Tangent, Parallel, Angle.

Geometry Problem 1399.
Triangle, Circumcircle, Perpendiculars, Angles, Congruence, Cyclic Quadrilateral.

Geometry Problem 1364.
Square, Inscribed Circle, Area, Angle Bisector, Perpendicular, 45 Degrees, Sketch, iPad Apps.

Geometry Problem 1363.
Square, Angle Bisector, Perpendicular, 45 Degrees, Angle, Sketch, iPad Apps.

Geometry Problem 1361.
Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps.

Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints.

Geometry Problem 1347.
Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle.

Problem 1341.
Geometry Problem 1341: Isosceles Triangle, 80-20-80 Degrees, Circumcenter, Angle Bisector.

Problem 1338.
Four Squares, Diagonals, Angle, 45 Degrees, Areas.

Problem 1336.
Right Triangle, Cevian, Double Angle, Perpendicular, 90 Degrees.

Geometry Problem 1329.
Two Squares Side by Side, Parallel, Perpendicular, 90 Degrees, Congruence.

Geometry Problem 1328.
Two Squares Side by Side, Perpendicular, 90 Degrees, Congruence.

Geometry Problem 1327.
Two Squares Side by Side, Perpendicular, 90 Degrees, Angle.

Geometry Problem 1326.
Triangle, Cevian, Incenters, Sum of Angles, 270 Degrees.

Geometry Problem 1324.
Quadrilateral, Diagonal, 45 Degrees, Angle Bisector, Isosceles Triangle, Congruence.

Geometry Problem 1323.
Square, Angle Trisector, Diagonal, Regular Dodecagon, Area, 30-60 degrees.

Geometry Problem 1322.
Triangle, Angle Bisector, Circumcircle, Chord, Secant, Sum of two Angles.

Geometry Problem 1299.
Triangles, Interior Point, Angles, 30 degrees.

Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint.

Geometry Problem 1297.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector.

Geometry Problem 1295.
Right Triangle, Incenter, Incircle, Excenter, Excircle, Congruence, Angle.

Geometry Problem 1288.
Triangle, 30-50-100 Degrees, Area, Inradius, Metric Relations, Measurement.

Geometry Problem 1287.
Triangle, 40-100-40 Degrees, Congruence, Area, Metric Relations, Measurement.

Geometry Problem 1286.
Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement.

Geometry Problem 1285.
Triangle, Quadrilateral, 60, 150, 90 Degree Angles, Congruence, Measurement.

Geometry Problem 1281.
Triangle, Circle, Diameter, Tangent, Altitude, Congruent Angles.

Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement.

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