Question #e2f89

2 Answers
Jul 23, 2015

That angle is equal to #30""^@#.

Explanation:

Here's how the image looks like

enter image source here

The first important thing you need to notice is that you're dealing with a regular hexagon, which means that all the interior angles are equal to #120""^@#.

So, if #angle(TUP)# is equal to #120""^@# and #TUV# is a straight line, then angle #angle(PUV)# is its complementary angle.

This means that

#angle(TUP) + angle(PUV) = 180""^@#

As a result,

#angle(PUV) = 180 - 120 = 60""^@#

Now, #triangleVUW# is a right triangle, as you can deduce from the fact that #angle(VUW)# is equal to #90^""@#.

Another important thing to notrice here is that #PUWV# is a parallelogram, which means that #bar(UN)# is parralel to #bar(WV)#

If this is the case, then #angle(PVU)# is equal to #90""^@# as well, since you're dealing with two parallel lines intersected by a straight line.

Moreover, #angle(PUV)# is equal to #angle(UVW)# for the same reason.

This means that

#angle(UVW) = angle(PUV) = 60""^@#

Therefore, #angle(VWU)# (angle #x#) will be

#angle(VWU) + angle(VUW) + angle(UVW) = 180""^@#

#angle(VWU) = 180 - 90 - 60 = color(green)(30""^@)#

Jul 23, 2015

#x = 30^o#

Explanation:

The interior angles of a regular hexagon are #120^o#
#rArr##color(white)("XXXX")##/_TUP = 120^o#

#/_TUP + /_PUV = 180^o#
#rArr##color(white)("XXXX")##/_PUV = 60^o#

Since #PU || VW#
#rArr##color(white)("XXXX")##/_PUV = /_UVW = 60^0#
#color(white)("XXXX")##color(white)("XXXX")#(opposite angles of a traversal crossing parallel lines [Euclid]

Since Sum of Interior Angles of a Triangle # = 180^o#
#rArr##color(white)("XXXX")##/_WUL + /_UVW + /_VWU = 180^o#

#rArr##color(white)("XXXX")##90^o + 60^o + /_VWU = 180^o#

#rArr##color(white)("XXXX")##/_VWU (= x) = 30^o#
enter image source here