The sum of measures of two alternate interior angles of two parallel lines with a transversal is 210°. what are the possible measures of the angles formed by the parallel lines and the transversal?

105 degrees

Step-by-step explanation:

Solution-

If the lines are parallel, then the alternate interior angles are congruent.

As the sum of measures of the two alternate interior angles = 210°

⇒ Measure of one alternate interior angles = 105°

Since a straight angle contains 180º, the two angles forming a linear pair also contain 180º when their measures are added (making them supplementary).

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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