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Example Questions
Example Question #1467 : Concepts
The measures of the angles of are as follows:
Is scalene, isosceles, or equilateral?
cannot exist
is equilateral
is isosceles but not equilateral
is scalene
is equilateral
The sum of the measures of the angles of a triangle is 180 degrees, so solve for in the equation:
A triangle with three 60-degree angles is equilateral.
Example Question #281 : Geometry
.
.
Is acute, right, or obtuse - or can it be determined?
is an obtuse triangle.
Whether is acute, right, or obtuse cannot be determined.
is a right triangle.
is an acute triangle.
is a right triangle.
The degree measures of the angles of a triangle total 180, so
Corresponding angles of similar triangles are congruent, so
is right, so
is a right triangle.
Example Question #283 : Geometry
in isosceles triangle
. Is this triangle acute, right, or obtuse?
is right
is obtuse
It is inconclusive whether is acute, right, or obtuse
is acute
It is inconclusive whether is acute, right, or obtuse
An isosceles triangle has at least two sides of equal measure, and also has at least two angles of equal measure.
One of two things can hold:
, so either of
or
has measure
. The third angle has measure
.
This angle, having measure greater than 90 degrees, is obtuse, so an obtuse triangle.
Alternatively, for some
, so
Since all three angles have measure less than 90 degrees, all three angles are acute, and is an acute triangle.
Therefore, the information is inconclusive.
Example Question #284 : Geometry
In parallelogram ,
, and
. Evaluate
.
and
are a pair of adjacent angles of the parallelogram, and as such, they are supplementary - that is, their degree measures total 180. Therefore,
Example Question #2061 : Hspt Mathematics
What is the total degrees of the angles in a square?
A square has four right angles which each have degrees.
To get the total you just multiple the measure of one by to get
.
Example Question #12 : Geometry
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 #663 : Geometry
If ,
, and
, what is the measure, in degrees, of
?
62
122
32
148
58
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.
Example Question #2062 : Hspt Mathematics
What is the slope of a line through the points and
?
Undefined slope
Use the slope fomula, setting
Example Question #2063 : Hspt Mathematics
In which quadrant, or on which axis, is the point with coordinates located?
Quadrant IV
Quadrant III
Quadrant II
The -axis
Quadrant I
Quadrant IV
Any point with a positive -coordinate and a negative
-coordinate is located in the lower right quadrant - Quadrant IV.
Example Question #2064 : Hspt Mathematics
Which of the following is an equation of a line with slope 0?
A line with slope 0 has equation for some real value
.
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