8.1: Angle Measurement

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An angle is a measure of the size of the opening of two lines that intersect. The VERTEX is the point of intersection, while the lines that form the opening are called the SIDES.

$clipboard_e141c2353b0c757ea6c6bcac7dab42c7d.png$

The angle can be called by

$clipboard_e888f2bff53ff82b010ad069f32789e87.png$

3 letters with the vertex in the middle: $\angle ABC$ or by the vertex only $\angle B$ or by a number or letter placed inside the angle.

There are 360 degrees in a circle. The angles are measured in degrees.

A Right Angle is 90 degrees or 1/4 of a circle. A Right Angle will look like the following.

$clipboard_e869260cce0cc1edffe2715b8b9053689.png$

An Acute Angle is an angle that is less than 90 degrees. The following are examples of Acute Angles

$clipboard_ed5d1474c2d3a0be945a1440f76032330.png$

An Obtuse Angle is an angle that is greater than 90 degrees and less than 180 degrees. The following are examples of Obtuse Angles.

$clipboard_e5268e965ee82123c6201c992d6ffb1a2.png$ $clipboard_e9baeca361a5b8171cebfeafd84011c07.png$

A Straight Angle is an angle equal to 180 degrees.

Vertical Angles

When two straight lines intersection they form four angles.

$clipboard_e0569523b489d88d75c2e4b99dae9ce5a.png$

Let’s say that $\angle A$ is 65 degrees, $\angle B$ is 115 degrees, $\angle C$ is 65 degrees, and $\angle D$ is 115 degrees

Did you notice that the opposite angles are equal in measurement? The opposite angles are also called Vertical Angles. When two straight lines cross or intersect, the Vertical Angles are always equal. A straight angle is 180 degrees.

$clipboard_e7bfbb927899472bbded993e390b88d50.png$

The angles W and X form a straight line, added together together they measure 180 degrees.

They are also know as Adjacent Angles. Adjacent Angles add up to 180 degrees. Adjacent Angles are also

$\angle Y$ and $\angle Z$,
$\angle W$ and $\angle Y$
$\angle X$ and $\angle Z$.

The three angles of a triangle will always add up to 180 degrees.

$clipboard_e9c486f40844a6c43420a34a17d29f9a2.png$

Lines Z and Y are parallel to each other. Line P the crosses both lines is called a Transversal.

$\angle C$ and $\angle F$ are called Alternate Interior Angles; They are equal in measurement.

$\angle D$ and $\angle E$ are also called Alternate Interior Angles.

$clipboard_ec8f849b540b4b045e96509c0689bb3be.png$

With the angle measuring 70 degrees, $\angle P$ will equal 110 degrees, their total equals 180 degrees.

$\angle P$ and $\angle Q$ are opposite angels so they equal 110 degrees because vertical angles are equal to each other.
$\angle P$ and $\angle T$ and corresponding angles so the both equal 110 degrees.
$\angle W$ equals 70 degrees because $\angle T$ plus $\angle W$ must equal a total of 180 degrees.

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