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Chapter 3: Q10 (page 80)

If m∠1=130what are the measures of the other numbered angels?

Short Answer

Expert verified

Measures of numbered angles are

m∠2=50;m∠3=50;m∠4=130;m∠5=130;m∠6=50;m∠7=50;andm∠8=130

Step by step solution

01

Step 1. Observations from figure

  • Arrowheads are shown on lines Iand P, so these lines are parallel
  • Line tis transversal to the parallel lines IandP
02

Step 2. Find m angle 2

∠1and ∠2forms linear pair, so sum of these angles is 180

m∠1+m∠2=180130+m∠2=180

m∠2=180−130

03

Step 3. Find m angle 3

∠2 and ∠3are vertically opposite angles, so there values are equal

m∠3=m∠2

Thus,m∠3=50

04

Step 4. Find m angle 4

∠1and ∠4are vertically opposite angles, so there values are equal

m∠4=m∠1

Thus,m∠4=130

05

Step 5. Find m angle 5, m angle 6, m angle 7, and m angle 8

Since, corresponding angles are equal

Pair of corresponding angles are

∠1−∠5,∠2−∠6,∠3−∠7,and∠4−∠8

Thus, measurement of these angles are

m∠5=130m∠6=50m∠7=50m∠8=130

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Most popular questions from this chapter

Find the values of x and y that make the lines shown in red parallel.

Alan tried to prove Postulate 10 as shown below. However, he did not have valid proof. Explain why not.

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

Given k∥l; transversal tcuts kand I

Prove: ∠1≅∠2

Statement

Reason

1.k∥l

Given

2.∠3≅∠2

If two parallel lines are cut by transversal then alt. int. ∠sare≅

3.∠1≅∠3

Vert. ∠sare≅

4.∠1≅∠2

Transitive Property

Complete. m∠6+m∠7+m∠8=?
  1. Draw two parallel lines and a transversal.
  2. Use a protractor to draw bisectors of two same-side interior angles.
  3. Measure the angles formed by the bisectors. What do you notice?
  4. Prove your answer to part (c).
  1. What is the measure of each interior angle of a regular pentagon?
  2. Can you tile a floor with tiles shaped like regular pentagons? (ignore the difficulty in tiling along the edges of the room.)
See all solutions

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