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In the figure above, if angle BAC = 80°, then z =

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In the figure above, if angle BAC = 80°, then z = [#permalink]

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New post 24 Aug 2017, 01:58
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In the figure above, if angle BAC = 80°, then z =

(A) 100
(B) 105
(C) 110
(D) 120
(E) 125

[Reveal] Spoiler:
Attachment:
2017-08-24_1249_003.png
2017-08-24_1249_003.png [ 9.98 KiB | Viewed 570 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, if angle BAC = 80°, then z = [#permalink]

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New post 24 Aug 2017, 02:47
Bunuel wrote:
Image
In the figure above, if angle BAC = 80°, then z =

(A) 100
(B) 105
(C) 110
(D) 120
(E) 125

[Reveal] Spoiler:
Attachment:
2017-08-24_1249_003.png


angle BAC = 80; hence x = 40
angle BCA = 30
hence angle ABC = 180-80-30 = 70
hence y= 35

z = 180 - 35 - 40 = 105
B
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Re: In the figure above, if angle BAC = 80°, then z = [#permalink]

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New post 24 Aug 2017, 04:11
2x=80, x=40
now in triangle ABC, total angle 80+2y+30=180; y=35
so in smaller triangle , x+y+z=180;40+35+z=180;z=105

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Re: In the figure above, if angle BAC = 80°, then z = [#permalink]

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New post 24 Aug 2017, 04:22
Bunuel wrote:
Image
In the figure above, if angle BAC = 80°, then z =

(A) 100
(B) 105
(C) 110
(D) 120
(E) 125

[Reveal] Spoiler:
Attachment:
2017-08-24_1249_003.png


Hi..
We do not require any other MEASURE of angle..
SUM of two other angles =angle A+angle B=2x+2y=180-30=150...X+y=75
Angle z= 180- x+y=180-75=105
B
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Re: In the figure above, if angle BAC = 80°, then z = [#permalink]

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New post 24 Aug 2017, 04:30
Bunuel wrote:
Image
In the figure above, if angle BAC = 80°, then z =

(A) 100
(B) 105
(C) 110
(D) 120
(E) 125

[Reveal] Spoiler:
Attachment:
2017-08-24_1249_003.png



x+y+z=180
2x=80, x=40
2y+80+30=180
2y=70, y=35
35+40+z=180
z=105

Answer is B
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Re: In the figure above, if angle BAC = 80°, then z = [#permalink]

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New post 29 Aug 2017, 16:22
Bunuel wrote:
Image
In the figure above, if angle BAC = 80°, then z =

(A) 100
(B) 105
(C) 110
(D) 120
(E) 125


Since angle BAC = 80 = 2x, x = 40.

We know that the sum of the interior angles of a triangle is 180 degrees. Thus, angle ABC = 180 - 30 - 80 = 70 = 2y, and so y = 35.

Since x = 40 and y = 35, angle z = 180 - 40 - 35 = 105.

Answer: B
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Re: In the figure above, if angle BAC = 80°, then z =   [#permalink] 29 Aug 2017, 16:22
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