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3. Lines m, n, and p are parallel. Line t intersects each line as shown, and the measure

of 21 is 143°.
a. Find the measure of 29.
11
12
b. Explain the angle relationships that verify the measure of 29.
c. Explain why 21 is congruent to 212 by using rigid motions.
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User Tbruyelle
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In the given setup with parallel lines and a transversal, angles 1, 2, 3, and 4 are congruent, each measuring 120 degrees, following the properties of corresponding angles, vertically opposite angles, and the angle sum on a straight line.

In the given diagram, lines l, m, and n are parallel, and p is a transversal. It is noted that the angle sum on a straight line is 180 degrees, and specifically, angle 4 is given as 60 degrees. This implies that angle 4 on the straight line with 60 degrees results in angle 4 being 120 degrees.

As per the properties of parallel lines and transversals, corresponding angles are equal. Therefore, angle 1 is equal to angle 4, and angle 2 is also equal to angle 1 as lines l and m are parallel, and p serves as a transversal. Consequently, angle 1, angle 2, and angle 4 are all equal, each measuring 120 degrees.

Furthermore, according to the property of vertically opposite angles, angle 3 is equal to angle 2. Since angle 4 is established as 120 degrees, it follows that angle 3 is also 120 degrees.

To summarize, angle 1, angle 2, angle 3, and angle 4 are all congruent, each measuring 120 degrees, as determined through the given properties of parallel lines, transversals, and the angle sum on a straight line.

The question probable may be:

In the figure l , m and n are parallel lines intersected by transversal p at X , Y and Z respectively. Find angle 1 , 2 and 3.

3. Lines m, n, and p are parallel. Line t intersects each line as shown, and the measure-example-1
User Njeru Cyrus
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