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Sub 505 (Easy)|   Geometry|      
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Bunuel
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In the figure above, if AB = BC, then n = 22 Oct 2019, 23:24
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90% (00:46) correct 10% (00:40) wrong based on 62 sessions

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In the figure above, if AB = BC, then n =

A. 30°
B. 40°
C. 50°
D. 60°
E. 70°


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C
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KSBGC
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In the figure above, if AB = BC, then n = 23 Oct 2019, 00:18
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Bunuel

In the figure above, if AB = BC, then n =

A. 30°
B. 40°
C. 50°
D. 60°
E. 70°


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Since , AB = BC, their angle must also be equal.

Angle B = 30

Angle A = 30.

BUT angle B is divided into 2 parts.

So, 30 + 80 + x = 180

x = 70.

Now,

30 + 30 + 70 + n = 180

n = 50.
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In the figure above, if AB = BC, then n = 17 Jul 2020, 22:12
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A = C = 30
ABD = 180-30-80 = 70
ABC = 180-30-30 = 120
n = 120-70 = 50

Hence, OA is (C).
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In the figure above, if AB = BC, then n = 18 Jul 2020, 07:55
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There are a few other ways to do this - for example:

ABC is isosceles, so the angle at C equals the angle at A, and the angle at C is 30 degrees.

The angles around point D must add to 180, because they lie in a straight line, so the angle on the right at point D is 100 degrees.

So we know two angles in the smaller triangle DBC are 30 and 100, and the missing angle, n, is 50 since the angles in a triangle sum to 180.
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