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Example Question #1591 : Basic Geometry
If lines A and B are parallel, what is the measurement of ?
Notice that and
are corresponding angles. This means that they possess the same angular measurements; thus, we can write the following:
Now, notice that and the provided angle of
angle are vertical angles. Vertical angles share the same angle measurements; therefore, we may write the following:
If and
, then
Example Question #51 : How To Find An Angle Of A Line
Angle measures
is the bisector of
is the bisector of
What is the measure of ?
Let's begin by observing the larger angle. is cut into two 10-degree angles by
. This means that angles
and
equal 10 degrees. Next, we are told that
bisects
, which creates two 5-degree angles.
consists of
, which is 10 degrees, and
, which is 5 degrees. We need to add the two angles together to solve the problem.
Example Question #521 : Plane Geometry
If ,
, and
, what is the measure, in degrees, of
?
58
122
32
148
62
148
The question states that . The alternate interior angle theorem states that if two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent; therefore, we know the following measure:
The sum of angles of a triangle is equal to 180 degrees. The question states that ; therefore we know the following measure:
Use this information to solve for the missing angle:
The degree measure of a straight line is 180 degrees; therefore, we can write the following equation:
The measure of is 148 degrees.
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