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Q45.

Expert-verified

Pre-algebra

Found in: Page 691

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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Short Answer

Multiple Choice: If $∠ 1$ and $∠ 2$ are complementary angles, what could their measures be?
$\begin{matrix} A . m ∠ 1 = 36 ° \\ m ∠ 2 = 24 ° \end{matrix}$ $\begin{matrix} B . m ∠ 1 = 52 ° \\ m ∠ 2 = 38 ° \end{matrix}$ $\begin{matrix} C . m ∠ 1 = 61 ° \\ m ∠ 2 = 61 ° \end{matrix}$ $\begin{matrix} D . m ∠ 1 = 89 ° \\ m ∠ 2 = 91 ° \end{matrix}$

The correct option is option B.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

It’s given that angle one and angle two are complimentary angles.

Step 2. Formula used.

The sum of complimentary angles is 90 degree.

Step 3. Calculation.

Now, add the angle and check that the sum of angles is 90 degree or not.

Option. A.

$36 {}^{\circ}+ 24 {}^{\circ}= 60 °$

This is the incorrect option.

Option B.

$52 {}^{\circ}+ 38 {}^{\circ}= 90 °$

This is the correct option.

Option C.

$61 {}^{\circ}+ 61 {}^{\circ}= 122 °$

This is not the correct option.

Option D.

$89 {}^{\circ}+ 91 {}^{\circ}= 180 °$

This is not the correct option.

Thus, the correct option is B.

Most popular questions for Math Textbooks

As shown in the diagram, the two structures of the Puerta de Europa (Door of Europe) in Madrid, Spain, lean toward each other at an angle of $15 °$ from the vertical.

In the diagram, $∠ 1$ and the angle that measures $15 °$ are complementary angles. Find $m ∠ 1$ .
Tell whether $∠ 1$ and $∠ 2$ are complementary or supplementary angles. Then use your answer to part (a) to find $m ∠ 2$ .

In Exercises 32 and 33, use the diagram.

What is $m ∠ 6$ ?

$30 °$ B. $60 °$ C. $90 °$ D. $120 °$

In Exercises 6 and 7, use the given information to find $m ∠ 2$ .

$∠ 1$ and $∠ 2$ are supplementary angles, and $m ∠ 1 = 160 °$ .

In Exercise 3-6, match the description with correct value.

Sum of measures of interior angles of a convex heptagon. $360 °$

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

$∠ 3 and ∠ 7$

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