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Example Questions
Example Question #792 : New Sat
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 #181 : Coordinate Geometry
If , , and , what is the measure, in degrees, of ?
62
148
32
122
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 #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.
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