Which statement is the converse of the following? if two angles form a linear pair, then they are supplementary. a. if two angles are supplementary, then they form a linear pair. b. if two angles do not form a linear pair, then they are not supplementary. c. if two angles are not supplementary, then they do not form a linear pair. d. if two angles form a linear pair, then they are supplementary.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

answer: do we write it

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4