Circle A is shown. Tangents L M and N M intersect at point M outside of the circle. Arc L N is 270 degrees. In the diagram of circle A, what is m? 75° 90° 120° 135°

Question

asked Apr 16, 2021 231k views

2 Answers

MKod · Answer 1 · 2021-04-21T10:01:28+0000

Answer:

$\angle m=90^o$

Explanation:

The picture of the question in the attached figure

we know that

The measurement of the external angle is the half-difference of the arches that comprise

so

$\angle m=(1)/(2)(major\ arc\ LN-minor\ arc\ LN)$

Remember that the sum of the major arc and a minor arc is equal to 360 degrees

we have

$major\ arc\ LN=270^o$ ----> is given

so

$minor\ arc\ LN=360^o-270^o=90^o$

substitute the values

$\angle m=(1)/(2)(270^o-90^o)=90^o$