A flashlight beam is reflected off of a mirror lying flat on the ground as shown in the picture below.(2x + 19)". How many degrees are in thez1 is congruent to 23, mz1=(x²+7) and m/2 =angle between the floor and the light beam?BIUE E X, x'

we have to find the angle between the floor and the light beam.m∠1=12x2+7°m∠2=2x2+19°sincem∠1=m∠3now…

Answered: 13, mz1=(x² +7) and mz2 (2x² + 19)".

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

A flashlight beam is reflected off of a mirror lying flat on the ground as shown in the picture below.
(2x + 19)". How many degrees are in the
z1 is congruent to 23, mz1=(x²+7) and m/2 =
angle between the floor and the light beam?
BIUE E X, x'

Expert Solution

Step 1

$w e h a v e t o f i n d t h e a n g l e b e t w e e n t h e f l o o r a n d t h e l i g h t b e a m . m ∠ 1 = {(\frac{1}{2} x^{2} + 7)}^{°} m ∠ 2 = {(2 x^{2} + 19)}^{°} \sin c e m ∠ 1 = m ∠ 3 n o w a s m ∠ 1, m ∠ 2, m ∠ 3 a r e l i n e a r p a i r s t h e r e f o r e m ∠ 1 + m ∠ 2 + m ∠ 3 = 180 ° {(\frac{1}{2} x^{2} + 7)}^{°} + {(2 x^{2} + 19)}^{°} + {(\frac{1}{2} x^{2} + 7)}^{°} = 180 ° {(x^{2} + 14)}^{°} + {(2 x^{2} + 19)}^{°} = 180 ° {(3 x^{2} + 33)}^{°} = 180 ° 3 x^{2} = 180 - 33 3 x^{2} = 147 x^{2} = \frac{147}{3} x^{2} = 49 x = 7 t h e a n g l e b e t w e e n t h e f l o o r a n d l i g h t b e a m m ∠ 1 = {(\frac{1}{2} {(7)}^{2} + 7)}^{°} m ∠ 1 = {(24.5 + 7)}^{°} = 31.5 °$

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