Let P be a point outside the circle such that triangle LMP has legs coincident with chords MW and LK (i.e. M, W, and P are colinear, and L, K, and P are colinear). By the intersecting secants theorem,

$m\angle LPM=\dfrac{m\widehat{LM}-m\widehat{WK}}2\impliesm\angle LPM=48^\circ$

The angles in any triangle add to 180 degrees in measure, and $\angle MLK\congruent\angle MLP$ and $m\angle LMW=m\angle LMP$ , so that

$m\angle MLK+m\angle LPM+m\angle LMP=180^\circ$

$\implies\boxed{m\angle LMW=67^\circ}$

6 0

3 years ago

Alex is constructing an inscribed square. Brittanie is constructing an inscribed equilateral triangle. In your own words, descri

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Alex is making a square with 4 corners, brittanie is making a triangle with 3 corners. That's the difference, hope it helped a little, it's not a full answer but maybe it will help.

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2 years ago