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Example Questions
Example Question #2 : How To Find An Angle
Note: Figure NOT drawn to scale.
In the above figure,
and . Which of the following is equal to ?
and form a linear pair, so their angle measures total . Set up and solve the following equation:
Example Question #261 : Geometry
Two angles which form a linear pair have measures
and . Which is the lesser of the measures (or the common measure) of the two angles?
Two angles that form a linear pair are supplementary - that is, they have measures that total
. Therefore, we set and solve for in this equation:
The two angles have measure
and
is the lesser of the two measures and is the correct choice.
Example Question #2041 : Hspt Mathematics
Two vertical angles have measures
and . Which is the lesser of the measures (or the common measure) of the two angles?
Two vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure. Therefore, we set up and solve the equation
Example Question #1 : Lines
A line
intersects parallel lines and . and are corresponding angles; and are same side interior angles.
Evaluate
.
When a transversal such as
crosses two parallel lines, two corresponding angles - angles in the same relative position to their respective lines - are congruent. Therefore,
Two same-side interior angles are supplementary - that is, their angle measures total 180 - so
We can solve this system by the substitution method as follows:
Backsolve:
, which is the correct response.
Example Question #262 : Geometry
Note: Figure NOT drawn to scale.
Refer to the above diagram. Give the measure of
.
The top and bottom angles, being vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure, so
,
or, simplified,
The right and bottom angles form a linear pair, so their degree measures total 180. That is,
Substitute
for :
The left and right angles, being vertical angles, have the same measure, so, since the right angle measures
, this is also the measure of the left angle, .Example Question #2 : Coordinate Geometry
What is the measurement of
?
If you extend the lines of the parellelogram, you will notice that a parellogram is the same as 2 different sets of parellel lines intersecting one another. When that happens, the following angles are congruent to one another:
Therefore,
Example Question #41 : Triangles
The three angles of a triangle are labeled
, , and . If is , what is the value of ?
Given that the three angles of a triangle always add up to 180 degrees, the following equation can be used:
Example Question #262 : Geometry
An isosceles triangle has a vertex angle of seventy degrees. What is the angle of one of the other angles?
A triangle has three sides and three angles, which add up to 180 degrees.
An isosceles triangle must have 2 equal sides and 2 equal base angles. Given the vertex angle is 70 degrees, subtract this angle by 180.
Since the other 2 base angles must equal to each other in an isoceles triangle, divide 110 with 2 to get the measure of the other angles.
The base angles must be
degrees each.As a check:
Example Question #2041 : Hspt Mathematics
What is the measure of an interior angle of a regular pentagon?
The formula to find the sum of total interior angles of a polygon is:
Since there are five sides in the pentagon, substitute
.
This is the sum of the interior angles of a pentagon. To find an interior angle, divide by five since there are five interior angles in a pentagon.
Example Question #11 : Geometry
is a straight line. intersects at point . If measures 120 degrees, what must be the measure of ?
None of the other answers
degrees
degrees
degrees
degrees
degrees
& must add up to 180 degrees. So, if is 120, (the supplementary angle) must equal 60, for a total of 180.
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