Question

in the triangle XYZ , draw a perpendicular bisector of XY to meet Xy at Q. Draw the bisector of angle ZXY to meet the perpendicular bisector at P. What is the size of angle ZPX?

Answer 1

Answer:

It will be an obtuse angle..

And the angle will be more than 90 deg. but less than 180 deg.

For measurement, let the angle named X be 2y

Then after bisecting it will be 2y/2 = y each

Now see the above fig. and see that in triangle PQX, 90+y+ <QPX = 180. (ASP)

<QPX = 180-90-y

<QPX = 90-y...............................(i)

Now in line ZQ ,<XPZ+ <QPX =180. (linear pair)

<XPZ=180-<QPX

<XPZ=180-(90-y)..................................(from i)

<XPZ=180-90+y

<XPZ=90+y

Thank you.........

Hope it helps...