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1. If ∠2 measures 120°, what is the measure of ∠1? Explain how you found the measure of ∠1.2. Think of the top and middle shelves as two lines cut by a transversal. What type of angles are ∠1 and ∠5?3. Use the relationship between ∠1 and ∠5 to decide whether the top and middle shelves are parallel.(Needs exterior angles)4. Is the bottom shelf parallel to the top shelf? Explain.5. Is the bottom shelf parallel to the middle shelf? Explain.

1 If 2 Measures 120 What Is The Measure Of 1 Explain How You Found The Measure Of 12 Think Of The Top And Middle Shelves As Two Lines Cut By A Transversal What class=

Sagot :

1.

The shelves can be assumed to be straight lines, and as straight lines have a 180° angle, then:

[tex]m\angle2+m\angle1=180\degree[/tex]

We know the value of m∠2. Thus, we can replace it and solve for m∠1:

[tex]120\degree+m\angle1=180\degree[/tex][tex]m\angle1=180\degree-120\degree[/tex][tex]m\angle1=60\degree[/tex]

2.

If we can suppose that the top and middle shelves are cut by a transversal, then ∠1 and ∠5 are corresponding angles.

3.

When two parallel lines are cut by a transversal, they form corresponding angles, and these are equal in measure. Therefore, as:

[tex]m\angle1=m\angle5=60\degree[/tex]

Then we can say that the top and middle shelves are parallel.

4.

As m∠11 = m∠2, we can say that they are alternate exterior angles, which are formed when parallel lines are cut by a transversal. Therefore, the bottom shelf is parallel to the top shelf.

5.

Finally, we can see that as m∠11 = 120°, we are in the same situation as in question 1, for which we conclude that m∠9 = 60°. Now, we have the same situation as in question 2, in which m∠5 and m∠9 are corresponding. Thus the bottom shelf is parallel to the middle shelf.

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