Q27 If 鈭燙聽and 鈭燚聽are complemen... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 2: Q27 (page 53)

If $鈭� C$ and $鈭� D$ are complementary, find the value of y, $m 鈭� C$ and $m 鈭� D$ .
$m 鈭� C = y - 8$ , $m 鈭� D = 3 y + 2$

Short Answer

Expert verified

The value of y is 24.

The measures of the angles C and D are 16掳 and 74掳.

Step by step solution

Step 1. Definition of complementary angles.

The complementary angles are the angles whose sum is 90掳.

Step 2. Write the relation between the angles C and D.

As the angles C andD are complementary, therefore, the sum of the angles C andD is 90掳.

Therefore, the relation between the angles C and D is: $m 鈭� C + m 鈭� D = 90 掳$

Step 3. Find the value of y.

Find the value of y by using the relation $m 鈭� C + m 鈭� D = 90 掳$ .

Therefore,

$m 鈭� C + m 鈭� D = 90 掳 y - 8 + 3 y + 2 = 90 4 y - 6 = 90 4 y = 90 + 6 4 y = 96 y = \frac{96}{4} y = 24$

Therefore, the value of y is 24.

Step 4. Find the measure of the angle C.

Substitute 24 for y into $m 鈭� C = y - 8$ to find the measure of the angle C.

Therefore,

$m 鈭� C = y - 8 \begin{matrix} = 24 - 8 \\ = 16 \end{matrix}$

Therefore, the measure of angle C is 16掳.

Step 5. Find the measure of the angle D.

Substitute 24 foryinto $m 鈭� D = 3 y + 2$ to find the measure of the angle D.

Therefore,

$m 鈭� D = 3 y + 2 = 3 脳 24 + 2 = 72 + 2 = 74$

Therefore, the measure of the angle D is 74掳.

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Statement	Reasons
1. A, M, and B have coordinated a, x, and b respectively; $b > a$ .	1. ?
2. $A M = x 鈭� a; M B = b 鈭� x$	2. ?
3. M is the midpoint of $\overset{炉}{A B}$ .	3. ?
4. $\overset{炉}{A M} 鈮� \overset{炉}{M B}$ , or $A M = M B$	4. ?
5. $x 鈭� a = b 鈭� x$	5. ?
6. $2 x =$ ?	6. ?
7. $x = \frac{a + b}{2}$	7. ?

91影视

If $鈭� C$ and $鈭� D$ are complementary, find the value of y, $m 鈭� C$ and $m 鈭� D$ .
$m 鈭� C = y - 8$ , $m 鈭� D = 3 y + 2$

Short Answer

Step by step solution

Step 1. Definition of complementary angles.

Step 2. Write the relation between the angles C and D.

Step 3. Find the value of y.

Step 4. Find the measure of the angle C.

Step 5. Find the measure of the angle D.

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91影视

If 鈭�Cand 鈭�Dare complementary, find the value of y, m鈭�Cand m鈭�D.m鈭�C=y-8,m鈭�D=3y+2

Short Answer

Step by step solution

Step 1. Definition of complementary angles.

Step 2. Write the relation between the angles C and D.

Step 3. Find the value of y.

Step 4. Find the measure of the angle C.

Step 5. Find the measure of the angle D.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Mechanics Maths

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

If $鈭� C$ and $鈭� D$ are complementary, find the value of y, $m 鈭� C$ and $m 鈭� D$ .
$m 鈭� C = y - 8$ , $m 鈭� D = 3 y + 2$