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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 01:31
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

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80% (02:27) correct 20% (02:49) wrong based on 79 sessions

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In the figure above angle, x is 10º. What is the measure of ∠z?

A. 40º
B. 45º
C. 60º
D. 85º
E. 100º

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C
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 01:56
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Quote:
In the figure above angle, x is 10º. What is the measure of ∠z?

A. 40º
B. 45º
C. 60º
D. 85º
E. 100º
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25 + y + (180 - z) = 180
z - y = 25

10 + z + (180 - 2y) = 180
z - 2y = -10

y + 25 = 2y - 10
y = 35
z = 25 + 35 = 60
Ans: C
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 02:12
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Angle ADB + Angle BDE + Angle EDF = 180°
10 + Angle BDE + 10 = 180
Angle BDE = 160

Also, In triangle BCD
Angle BDE + Angle EDF = Z+(180-2y) {exterior angle}
180-2y+Z = 170
10-2Y+Z = 0 ---------(1)

In triangle ABC
25+Y+180-Z = 180
25+Y-Z = 0 --------(2)

equating both equations
Y = 35
Angle CBD = 180-2Y
=> 180-2(35)
=> 180-70 = 110

Z = 180-BDC-CBD
Z = 180-10-CBD
Z = 180-120
Z = 60

Answer is C
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 02:28
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∠x=10
∠z= 25º+∠y
∠y+∠y+∠a=180º
∠z+∠a+∠x=180º

Let`s define ∠z and ∠a in terms of y
25+y+180-2y+10=180 => y=35 => ∠z=25+35=60
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 03:25
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We have,
z + x + 180 - 2y = 180
=> z + 10 - 2y = 0
=> z -2y = -10 --------i
z = 25 + y (exterior angle property)
=> z - y = 25
=> 2z - 2y = 50 ----------ii

Subtracting i from ii,
z = 60
Hence, OA is (C).
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 04:52
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using exterior interior angle relation,
z=25+y --->1

and in triangle with line zx,
z+x+180-2y=180
z+x=2y ---->2

sub 2 in 1,
we get z=60

Ans C
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 06:36
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IMO C
Refer attached image.
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 11:34
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Step 1: Understanding the question
Angle z is an exterior angle of triangle ABC.
Also measure of angle BCD = 180-2y (linear pair)

Step 2: Calculation
z = y + 25 (exterior angle property)
y = z - 25 ----(I)

x+ z + (180 - 2y) = 180
x + z = 2y
x + z = 2(z - 25)
10 + z = 2z - 50
z = 60

IMO C
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In the figure above angle, x is 10º. What is the measure of ∠z? 23 Jul 2020, 20:14
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Quote:
In the figure above angle, x is 10º. What is the measure of ∠z?

A. 40º
B. 45º
C. 60º
D. 85º
E. 100º
Show more

z+10+a=180
2y+a=180

25+y+180-z=180
25+y-z=0
z=25+y

(25+y)+10+a=180
y+a=145

2y+a=180
-[y+a=145]
y=35
z=25+35=60

Ans (C)
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