HSPT Math : HSPT Mathematics
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Example Questions
Example Question #6 : How To Find An Angle
Two vertical angles have measures 
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 #5 : Lines
A line 
Evaluate 
When a transversal such as 
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:
Example Question #1 : How To Find An Angle
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 
The left and right angles, being vertical angles, have the same measure, so, since the right angle measures 
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 #2042 : Hspt Mathematics
The three angles of a triangle are labeled 
Given that the three angles of a triangle always add up to 180 degrees, the following equation can be used:
Example Question #2041 : Hspt Mathematics
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 
As a check:
Example Question #2042 : 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
None of the other answers
Example Question #1451 : Concepts
Find the total interior degrees in an octagon.
To solve, simply use the formula for the total of the interior angles where n is the number of vertices.
In this particular case 
Thus,
Example Question #1453 : Concepts
Two angles are supplementary. The measure of one angle is 23 degrees less than twice that of the second. Give the lesser of the measures of the two angles.
Let 
The other angle has measure 
The lesser of the two measures is requested, so the correct response is 
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