In rectangle ABCD below, mZAED = y + 10 and MZAEB = 4y30. Findthe mZADE.CEBAnswer: MZADE =Submit Answerattempt 1 out of 2/ problem 1 out of max 1

Answered: In rectangle ABCD below, mZAED = y + 10…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

In rectangle ABCD below, mZAED = y + 10 and MZAEB = 4y
30. Find
the mZADE.
C
E
B
Answer: MZADE =
Submit Answer
attempt 1 out of 2/ problem 1 out of max 1

Expert Solution

Step 1

Given Data:

The measure of angle AED is: $m ∠ A E D = y + 10$

The measure of angle AEB is: $m ∠ A E B = 4 y - 30$

The ∠AED and ∠AEB are angles of linear pair.

The sum of ∠AED and ∠AEB is,

$m ∠ A E D + m ∠ A E B = 180 °$

Substitute the values in the above equation.

$\begin{array}{rcl} y + 10 + 4 y - 30 & = & 180 \\ 5 y - 20 & = & 180 \\ 5 y & = & 200 \\ y & = & 40 ° \end{array}$

Step 2

The magnitude of ∠AED is,

$m ∠ A E D = y + 10$

Substitute the value in the above equation.

$\begin{array}{rcl} m ∠ A E D & = & 40 + 10 \\ = & 50 ° \end{array}$

The magnitude of ∠AEB is,

$m ∠ A E B = 4 y - 30$

Substitute the value in the above equation.

$\begin{array}{rcl} m ∠ A E B & = & 4 (40) - 30 \\ = & 160 - 30 \\ = & 130 ° \end{array}$

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In rectangle ABCD below, mZAED = y + 10 and mZAEB = 4y – 30. Find %3D the MZADE. C E A' 'B