In triangle ABC, AD =DB=DC (see figure). If angle DCB is $60^{o}$ and angle ACD is $20^{o}$ , what is the value of x?

20

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40

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10

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50

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Solution

The correct option is A $10$
If AD = DB = DC, then the three triangular regions in this figure are all isosceles triangles. Therefore, you can fill in some of the missing angle measurements as shown to the right. Since you know that there are $180^{o}$ in the large triangle ABC, you can write the following equation:
$x + x + 20 + 20 + 60 + 60 = 180$
$2 x + 160 = 180$
$x = 10$

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In triangle ABC, AD =DB=DC (see figure). If angle DCB is 60o and angle ACD is 20o, what is the value of x?

In triangle ABC, AD =DB=DC (see figure). If angle DCB is $60^{o}$ and angle ACD is $20^{o}$ , what is the value of x?