Question

In order to answer the question correctly, please use the following image below:

Describe the error in finding the angle measure.

Find the correct angle measure.

m∠SUT=(blank)

What is the error in finding the angle measure? What is the correct angle measurement of SUT?

Please show all the work on how you got your answers.(Note: If you are unable to explain your work then it's fine. All that I am asking for is for the work to be shown so I can see how you got your answers)

Answer 1

1) A

2) 41.5°

Explanation:

SUT would have been 46° if U was the centre

Angle SUT = (37+46)/2

= 83/2

= 41.5

Answer 2

see below

Explanation:

The angle where chords cross is the average of the intercepted arcs. Here, that is ...

(37° +46°)/2 = (83°)/2 = 41.5°

Angle SUT is 41.5°.

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Comment on the error

The measure of an arc cannot be arbitrarily said to be the same as the angle where the chords cross. It will be the same if (a) the chords cross at the circle center, or (b) the opposite intercepted arc has the same measure. Neither of these conditions hold here.