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# Geometry

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Line MS and line TS are tangent to circle R.

A. What is the measure, in degrees, of ∠MRT?

B. What is the measure, in degrees, of ∠MAT?

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Feb 24, 2019

#1
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Line MS and line TS are tangent to circle R.

A. What is the measure, in degrees, of ∠MRT?

B. What is the measure, in degrees, of ∠MAT?

Draw the line from S to R.  This gives you 16.5o out there in each of the two triangles that are formed.

A tangent to a circle is perpendicular to the radius drawn to the point, so that gives you 90o in each triangle.

So angle MRS is 180o – (90o + 16.5o) = 73.5o

Similarly TRS is also 73.5o

Add angles MRS and TRS = 73.5o + 73.5o  to get angle MRT is 147o

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Feb 24, 2019
#2
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But what are the measures of the angles listed?

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Thank you!

JoseyP  Feb 24, 2019
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B.

Since MRT is a central angle =  147°.....then MAT is an inscribed angle subtending the same arc...so it measures (1/2)147  =   73.5°

Feb 24, 2019
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Thank you

JoseyP  Feb 24, 2019