If MZABD = 72°, what are MZABC and mZDBCc?(5x+3)° D(8x-9)BMZABC =

Answered: If MZABD = 72°, what are MZABC and…

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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If MZABD = 72°, what are MZABC and mZDBCc?
(5x+3)° D
(8x-9)
B
MZABC =

Expert Solution

Step 1

Given: $m ∠ A B D = 72 °$ .

To find: $m ∠ A B C$ and $m ∠ D B C$ .

Solution:

From the figure, we have $m ∠ A B C = (8 x - 9) °$ and $m ∠ D B C = (5 x + 3) °$ .

Now, we can find that $m ∠ A B D = m ∠ A B C + m ∠ D B C$

$\begin{array}{rcl} m ∠ A B D & = & m ∠ A B C + m ∠ D B C \\ 72 ° & = & (8 x - 9) ° + (5 x + 3) ° \\ 72 & = & 8 x - 9 + 5 x + 3 \\ 72 & = & 13 x - 6 \\ 13 x & = & 72 + 6 \\ 13 x & = & 78 \\ x & = & \frac{78}{13} \\ x & = & 6 \end{array}$

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If MZABD = 72°, what are MZABC and mZDBCc? (5x+3)° D (8x-9) B MZABC =