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Chapter 12: Q9. (page 689)

Use the diagram shown. Identify all pairs of the specified angles.

Complementary angles

Short Answer

Expert verified

In the quadrilateral, ∠Aand∠D form a complementary angle pair.

Step by step solution

01

Step 1. Given Information.

The figure is shown below.

02

Step 2. Concept used.

If the sum of two angles is 90° then the angles are called complementary angles and if the sum is 180° then the angles are called supplementary angles.

03

Step 3. Calculation.

The sum of measures of all the possible pairs of angles in the quadrilateral is,

∠A+∠B=170°∠A+∠C=180°∠A+∠D=90°∠B+∠C=270°

And,

∠B+∠D=180°∠C+∠D=190°

In the above list, only the pair ∠A,and∠D have the sum of their measures equal to 90°.

04

Step 4. Conclusion.

The pair of complementary angles in the quadrilateral is ∠A,and∠D.

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Most popular questions from this chapter

Use the given information to find m∠2.

∠1 and ∠2 arecomplementary angles, and m∠1=81°.

Tell whether the angles are corresponding, alternate, interior, or alternate exterior angles.

∠2and∠7

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

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

Describe the pattern. (P.772)

1,5,25,125,…

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

m∠5=24°m∠6=66°
See all solutions

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