#1**+2 **

Since it is an equilateral triangle, each of the interior angles is 60^{o}.

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 90^{o}.

The angle at the center of the circle is 60^{o}.

Therefore, angle(x) is 30^{o}.

geno3141 Apr 30, 2020

#2**+1 **

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 60^{o}

On the right of the diagram,

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

On the left of the diagram,

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

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

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Guest Apr 30, 2020