Solving for Unknown Angles Transversals
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Name ______Date ______Ms. Moorer Geometry
Solving for Unknown Angles – Transversals
Opening Exercise Use the diagram at the right to determine and . and are straight lines. = ______= ______Name a pair of vertical angles: ______
Find the measure of . Justify your calculation. ______
Relevant Vocabulary Alternate Interior Angles: Let line be a transversal to lines and such that intersects at point and intersects at point . Let be a point on , and be a point on such that the points and lie in opposite half-planes of . Then the angle and the angle are called alternate interior angles of the transversal with respect to and . Corresponding Angles:Let line be a transversal to lines and .If and are alternate interior angles, and and are vertical angles, then and are corresponding angles.
Example 1 Given a pair of lines and in a plane (see the diagram below), a third line is called a transversal if it intersects at a single point and intersects at a single but different point. The two lines and are parallel if and only if the following types of angle pairs are congruent or supplementary:
. Corresponding Angles are equal in measure
______. Alternate Interior Angles are equal in measure
______. Same Side Interior Angles are supplementary
______a. b.
= ______= ______c. d.
= ______= ______
Exercises In each exercise below, find the unknown (labeled) angles. Give reasons for your solutions.
1. = ______
= ______
= ______
2. = ______
= ______
#1-8: Using the figure at the right, find the measure of the angle if : 1) 2)
3) 4)
5) 6)
7) 8) #9-12: Using the figure at the right, find the value of x and the indicated angle if :
9) 10)
11) 12)
#13-18) If , and lines a and b are cut by transversal c, a) Identify the relationship between the angles b) Find x: 13) 14) 15) 16)
17) 18)