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Example Questions
Example Question #9 :Lines
In the following diagram, lines一个dare parallel to each other. What is the value for?
It cannot be determined
当两条平行线相交line, the sum of the measures of the interior angles on the same side of the line is 180°. Therefore, the sum of the angle that is labeled as 100° and angle y is 180°. As a result, angle y is 80°.
Another property of two parallel lines that are intersected by a third line is that the corresponding angles are congruent. So, the measurement of angle x is equal to the measurement of angle y, which is 80°.
Example Question #11 :Intersecting Lines And Angles
服用角的测量是40度rees larger than twice the measure of the complement of angle A. What is the sum, in degrees, of the measures of the supplement and complement of angle A?
140
90
50
190
40
190
Let A represent the measure, in degrees, of angle A. By definition, the sum of the measures of A and its complement is 90 degrees. We can write the following equation to determine an expression for the measure of the complement of angle A.
A + measure of complement of A = 90
Subtract A from both sides.
measure of complement of A = 90 – A
Similarly, because the sum of the measures of angle A and its supplement is 180 degrees, we can represent the measure of the supplement of A as 180 – A.
The problem states that the measure of the supplement of A is 40 degrees larger than twice the measure of the complement of A. We can write this as 2(90-A) + 40.
Next, we must set the two expressions 180 – A and 2(90 – A) + 40 equal to one another and solve for A:
180 – A = 2(90 – A) + 40
Distribute the 2:
180 - A = 180 – 2A + 40
Add 2A to both sides:
180 + A = 180 + 40
Subtract 180 from both sides:
A = 40
Therefore the measure of angle A is 40 degrees.
The question asks us to find the sum of the measures of the supplement and complement of A. The measure of the supplement of A is 180 – A = 180 – 40 = 140 degrees. Similarly, the measure of the complement of A is 90 – 40 = 50 degrees.
The sum of these two is 140 + 50 = 190 degrees.
Example Question #11 :Act Math
is a straight line.intersectsat point. Ifmeasures 120 degrees, what must be the measure of?
degrees
degrees
degrees
None of the other answers
degrees
degrees
&must add up to 180 degrees. So, ifis 120,(the supplementary angle) must equal 60, for a total of 180.
Example Question #12 :Act Math
Two parallel lines are intersected by a transversal. If the minor angle of intersection between the first parallel line and the transversal is, what is the minor angle of intersection between the second parallel line and the transversal?
When a line intersects two parallel lines as a transversal, it always passes through both at identical angles (regardless of distance or length of arc).
Example Question #11 :Geometry
If,, and, what is the measure, in degrees, of?
148
58
122
62
32
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 ofis 148 degrees.
Example Question #15 :Act Math
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,一个dwhich 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.