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# What is the sum of the indicated angles above?

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
What is the sum of the indicated angles above?  [#permalink]

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07 Sep 2018, 00:00
00:00

Difficulty:

35% (medium)

Question Stats:

58% (01:45) correct 42% (01:38) wrong based on 41 sessions

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What is the sum of the indicated angles above?

A. 1080
B. 900
C. 810
D. 720
E. 540

Attachment:

image013.jpg [ 2.88 KiB | Viewed 496 times ]

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Re: What is the sum of the indicated angles above?  [#permalink]

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07 Sep 2018, 02:19
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The three lines from a triangle.
let the angles of the triangle be e, f, g starting from the point that contains angles x, y, z.
The sum of internal angles of a triangle is 180.

Now, $$x+y+z+d=360$$,
Similarly, $$a+b+c+e=360$$
&, $$p+f+n+m=360$$

Adding all the three equations, we get:
$$x+y+z+a+b+c+p+m+n+(d+e+f)=360*3$$
$$d+e+f=180$$
$$this implies, x+y+z+a+b+c+p+m+n=1080-180$$
=900.

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Re: What is the sum of the indicated angles above?  [#permalink]

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08 Sep 2018, 04:49
Bunuel wrote:

What is the sum of the indicated angles above?

A. 1080
B. 900
C. 810
D. 720
E. 540

Attachment:
image013.jpg

a) The sum of exterior angles of a triangle is 360°
So, (y+c+p)+(z+m+a)=360+360=720°
b) The sum of the interior angles of a triangle is 180°.
So, x+n+b=180°
Sum of the indicated angles=(y+c+p)+(z+m+a)+(x+n+b)=720°+180°=900°

Ans. (B)
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Re: What is the sum of the indicated angles above?  [#permalink]

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08 Sep 2018, 22:44
Bunuel wrote:

What is the sum of the indicated angles above?

A. 1080
B. 900
C. 810
D. 720
E. 540

Attachment:
image013.jpg

Sum of exterior angles of a polygon = 360 deg.
y+c+p=360 (Angle formed by extension of one side and the other side)
Similarly, a+z+m=360
x+b+n=180 (Sum of the angles of the triangle)
Adding the three equations we get the desired result = 900
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Re: What is the sum of the indicated angles above?   [#permalink] 08 Sep 2018, 22:44
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