All HSPT Math Resources
Example Questions
Example Question #2001 : Hspt Mathematics
What is the measure of a right angle?
The measure of a right angle is degrees.
Example Question #1405 : Concepts
Figure NOT drawn to scale.
If and , evaluate .
More information is needed to solve the problem.
The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so
Example Question #106 : Properties Of Triangles
Figure NOT drawn to scale.
If and , evaluate .
The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so
Example Question #2002 : Hspt Mathematics
If the vertex angle of an isoceles triangle is , what is the value of one of its base angles?
In an isosceles triangle, the base angles are the same. Also, the three angles of a triangle add up to .
So, subtract the vertex angle from . You get .
Because there are two base angles you divide by , and you get .
Example Question #2003 : Hspt Mathematics
Note: Figure NOT drawn to scale.
Refer to the above diagram.
Which of the following could be a measure of ?
All of the other choices give a possible measure of .
The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so
.
We also have the following constraints:
Then, by the addition property of inequalities,
Therefore, the measure of must fall in that range. Of the given choices, only falls in that range.
Example Question #109 : Properties Of Triangles
Refer to the above diagram.
Which of the following could be a measure of ?
All of the other responses are correct.
All of the other responses are correct.
The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so
or
Therefore, the maximum value of is the least possible value of subtracted from the greatest possible value of :
The minimum value of is the greatest possible value of subtracted from the least possible value of :
Therefore,
Since all of the choices fall in this range, all are possible measures of .
Example Question #1411 : Concepts
One angle of a right triangle has measure . Give the measures of the other two angles.
This triangle cannot exist.
This triangle cannot exist.
A right triangle must have one right angle and two acute angles; this means that no angle of a right triangle can be obtuse. But since , it is obtuse. This makes it impossible for a right triangle to have a angle.
Example Question #2 : How To Find An Angle In A Right Triangle
One angle of a right triangle has measure . Give the measures of the other two angles.
This triangle cannot exist.
One of the angles of a right triangle is by definition a right, or , angle, so this is the measure of one of the missing angles. Since the measures of the angles of a triangle total , if we let the measure of the third angle be , then:
The other two angles measure .
Example Question #2004 : Hspt Mathematics
AB and CD are two parrellel lines intersected by line EF. If the measure of angle 1 is , what is the measure of angle 2?
The angles are equal. When two parallel lines are intersected by a transversal, the corresponding angles have the same measure.
Example Question #2 : How To Find An Angle Of A Line
Lines A and B in the diagram below are parallel. The triangle at the bottom of the figure is an isosceles triangle.
What is the degree measure of angle ?
Since A and B are parallel, and the triangle is isosceles, we can use the supplementary rule for the two angles, and which will sum up to . Setting up an algebraic equation for this, we get . Solving for , we get . With this, we can get either (for the smaller angle) or (for the larger angle - must then use supplementary rule again for inner smaller angle). Either way, we find that the inner angles at the top are 80 degrees each. Since the sum of the angles within a triangle must equal 180, we can set up the equation as
degrees.