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 Apr 30, 2020
 #1
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Since it is an equilateral triangle, each of the interior angles is 60o.

 

Look at the large triangle  -- from the center of the circle to the point of tangency to the exterior vertex.

The angle formed by the radius and the tangent is 90o.

The angle at the center of the circle is 60o.

Therefore, angle(x) is 30o.

 Apr 30, 2020
 #2
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I can't draw on this site, or I'd label the diagram.  I'll try to explain it with words. 

 

The inside triangle is equilateral so all its angles are 60o  

 

On the right of the diagram,

the angle of the outside triangle is supplemental to 60o so it's 120o  

 

On the left of the diagram,

the tangent is perpendicular to the radius,so the supplemental angle of the outside triangle is 90o – 60o = 30o 

 

The sum of those two angles is 150o.  All the angles of any triangle total 180o so x is 180o – 150o = 30o  

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 Apr 30, 2020

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