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Angles

Description:

Angle questions test your ability to use the laws of vertical and alternate angles to solve for unknown angles.

Approach:

Remember, if the question doesn't say “Figure Not Drawn to Scale,” you can generally come up with a very accurate estimate of the angle. Harder questions require you to work through several angles in order to arrive at the correct answer.


1) Lines

Straight lines are always made up of 180° angles.


2) Vertical Angles

Vertical angles are opposite angles formed by the intersection of any two lines. Vertical angles are always equal to one another.

[Image: Vertical angles]

In this example: A = B and C = D


3) Angles Formed by Parallel Lines

When two parallel lines are intersected by a third straight line, all of the small angles created are equal to one another. Additionally, all of the large angles created are equal to one another.

[Image: Angles of parallel lines]


4) Triangles

The sum of the measures of the interior angles of any triangle is always 180°.

[Image: Interior angles of a triangle sum to 180°]

In this example:

a + b + c = 180°


5) Circles

Circles measure 360°.

[Image: Circles measure 360°]


6) Polygons

The sum of a polygon's interior angles = (Number of Sides - 2) * 180°

You can also count the number of triangles you can draw from one vertex inside the polygon and multiply by 180°.

Hexagon: 6 sides.

[Image: Hexagon]

Use this equation: (6 - 2) * 180° = 720°

Now draw the triangles to confirm. How many are there?

The sum of the exterior angles of any polygon is always 360°, no matter how many sides it has.


7) Practice:

  • How many degrees are in each interior angle of an octagon?
  • How many degrees are in each exterior angle of a hexagon?
  • How many degrees are inside of a pentagon?

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