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Chapter 12: Q33. (page 696)

In Exercises 32 and 33, use the diagram.

Which numbered angles have the same measure as 鈭�1? Explain your reasoning.

Short Answer

Expert verified

m鈭�1=m鈭�3=m鈭�4=m鈭�7

Step by step solution

01

Step 1. Given Information.

The figure is shown below.

02

Step 2. Concept Used.

In the parallel line and its transversal corresponding angles are equal, vertically opposite angles are equal and also alternate exterior angles are equal.

03

Step 3. Explanation.

In the diagram,

m鈭�1=m鈭�3 (Vertically opposite angles)

m鈭�1=m鈭�4 (Corresponding angles)

m鈭�1=m鈭�7 (Alternate exterior angles)

Thus, m鈭�1=m鈭�3=m鈭�4=m鈭�7.

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Most popular questions from this chapter

Tell whether the angles are complementary, supplementary, or neither.

m鈭�1=63掳m鈭�2=27掳

Draw a quadrilateral and show one exterior angle at each vertex.

Use the given information to find m鈭�2.

鈭�1 and 鈭�2 arecomplementary angles, and m鈭�1=81掳.

Extended Problem Solving: In the bicycle frame shown, 鈭�1is called the head angle, and 鈭�2 is called the seat angle. Lines mand nare parallel.

  1. Identify: Are 鈭�1 and 鈭�2 are corresponding, alternate interior, or alternate exterior angles.
  2. Explain: 鈭�1 and 鈭�2 have the same measure?
  3. Calculate: 鈭�1 and 鈭�2.Explain how you got your answer.

A transversal intersects lines mand n. If the corresponding angles are congruent, what can you conclude about lines m and n?
See all solutions

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