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# Geometry Concepts: GED Test Prep (page 2)

By LearningExpress Editors
LearningExpress, LLC
Updated on Mar 9, 2011

### Classifying Angles

Angles can be classified into the following categories: acute, right, obtuse, and straight.

• An acute angle is an angle that measures less than 90 degrees.
• A right angle is an angle that measures exactly 90 degrees. A right angle is represented by a square at the vertex.
• An obtuse angle is an angle that measures more than 90 degrees, but less than 180 degrees.
• A straight angle is an angle that measures 180 degrees. Thus, both of its sides form a line.

### Complementary Angles

Two angles are complementary if the sum of their measures is equal to 90 degrees.

### Supplementary Angles

Two angles are supplementary if the sum of their measures is equal to 180 degrees.

Adjacent angles have the same vertex, share a side, and do not overlap.

The sum of all of the measures of adjacent angles around the same vertex is equal to 360 degrees.

### Angles of Intersecting Lines

When two lines intersect, two sets of nonadjacent angles called vertical angles are formed. Vertical angles have equal measures and are supplementary to adjacent angles.

• m1 = m3 and m2 = m4
• m1 = m4 and m3 = m2
• m1 + m2 = 180 and m2 + m3 = 180
• m3 + m4 = 180 and m1 + m4 = 180

### Bisecting Angles and Line Segments

Both angles and lines are said to be bisected when divided into two parts with equal measures.

Example

Line segment AB is bisected at point C.

According to the figure, A is bisected by ray AC.

### Angles Formed by Parallel Lines

• When two parallel lines are intersected by a third line, vertical angles are formed.
• Of these vertical angles, four will be equal and acute, and four will be equal and obtuse.
• Any combination of an acute and an obtuse angle will be supplementary.

In the previous figure:

• b, c, f, and g are all acute and equal.
• a, d, e, and h are all obtuse and equal.
• Also, any acute angle added to any obtuse angle will be supplementary.

Examples

mb + md = 180°

mc + me = 180°

mf + mh = 180°

mg + ma = 180°

Example

In the following figure, if m||n and a||b, what is the value of x?

Solution

Because both sets of lines are parallel, you know that x° can be added to x + 10 to equal 180. The equation is thus x + x + 10 = 180.

Example

Solve for x:

Therefore, mx = 85 and the obtuse angle is equal to 180 – 85 = 95.

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