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555-605 (Medium)|   Geometry|      
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Bunuel
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ABCDEFGHI is a regular polygon with nine sides. What is the measure in 09 Dec 2015, 08:52
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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)

Question Stats:

75% (01:44) correct 25% (02:03) wrong based on 117 sessions

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ABCDEFGHI is a regular polygon with nine sides. What is the measure in degrees of angle ACB?

A. 18
B. 20
C. 25
D. 27
E. 30

Source: GMATQuantum
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B
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ABCDEFGHI is a regular polygon with nine sides. What is the measure in 09 Dec 2015, 09:15
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Bunuel
ABCDEFGHI is a regular polygon with nine sides. What is the measure in degrees of angle ACB?

A. 18
B. 20
C. 25
D. 27
E. 30

Source: GMATQuantum
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Hi,
the formula of sum of angles in a polygon of sides n=(n-2)*180
so sum of angles=7*180..
therefore each angle ,angle ABC=7*180/9=140..
when we join A and C to make a triangle ABC, it becomes an isosceles triangle with AB and BC equal..
so angle ACB=angleCAB=(180-140)/2=20..
ans B
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ABCDEFGHI is a regular polygon with nine sides. What is the measure in 09 Dec 2015, 09:35
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Bunuel
ABCDEFGHI is a regular polygon with nine sides. What is the measure in degrees of angle ACB?

A. 18
B. 20
C. 25
D. 27
E. 30

Source: GMATQuantum
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i am getting 20 (choice B)

triangle BAC should form an isoscles triangle.

angle ABC is 140 deg ( total 9 angles to the polygon. so 1260/9=140)

angle BAC = angle BCA = x ( isosceles traingle)

so ; 140+ x+ x = 180

2x=40

x=20

hence answer B

what is the OA?
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ABCDEFGHI is a regular polygon with nine sides. What is the measure in 16 Jan 2017, 15:16
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Bunuel
ABCDEFGHI is a regular polygon with nine sides. What is the measure in degrees of angle ACB?

A. 18
B. 20
C. 25
D. 27
E. 30

Source: GMATQuantum
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(9-2)(180)=1260°
1260/9=140°=∠ABC
side AB=BC; triangle is isosceles
180-140=40°=2*∠ACB
∠ACB=20°
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ABCDEFGHI is a regular polygon with nine sides. What is the measure in 18 Jan 2017, 10:12
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Bunuel
ABCDEFGHI is a regular polygon with nine sides. What is the measure in degrees of angle ACB?

A. 18
B. 20
C. 25
D. 27
E. 30
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Let us draw a figure to make things clearer:



Since polygon ABCDEFGHI is a regular polygon, we know that the interior angles are of equal measure. We can use the following formula to determine the sum of the interior angles of polygon ABCDEFGHI:

sum of interior angles = 180(number of sides - 2)

sum = 180(9 - 2)

sum = 180(7) = 1260

Since there are nine angles, each angle measures 1260/9 = 140 degrees

This is the measurement of angle ABC. In triangle ABC, since angle ABC is 140, the sum of angles ACB and CAB is 180 - 140 = 40. Furthermore, since ABC is an isosceles triangle, angle ACB is 40 / 2 = 20.

Answer: B
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ABCDEFGHI is a regular polygon with nine sides. What is the measure in 26 Feb 2020, 02:19
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