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Q9.

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Pre-algebra
Found in: Page 689
Pre-algebra

Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

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Illustration

Short Answer

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

Complementary angles

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Given Information.

The figure is shown below.

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.

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°.

Step 4. Conclusion.

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

Most popular questions for Math Textbooks

Multiple Choice: If ∠1 and ∠2 are complementary angles, what could their measures be?

A. m∠1=36°m∠2=24° B. m∠1=52°m∠2=38° C. m∠1=61°m∠2=61° D. m∠1=89°m∠2=91°

The drawing is a herring illusion, in which intersecting transversal make two parallel lines appear to be curves. Describe a way you can use a protector to verify that the two lines are parallel.

Find the sum of the measures of the interior angles of a convex 10-gon.

Extended Problem Solving: In the bicycle frame shown, ∠1 is called the head angle, and ∠2 is called the seat angle. Lines m and n are 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.

Find m∠1.
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