in a parallelogram WXYZ, angle WXY = 72 degrees, angle ZWY = 80 degrees. calculate; angle WZY, angle XWZ and angle WYZ

Question

GEOMETRY OF O LEVELS

Answer 1

Hi Ash!

 

So, it looks like you're trying to find the angles created by criss-crossing the parallelogram, so:

 

First, draw and label the shape.

 

Then, figure out the rest of the angles of the parallelogram itself. Since the opposite angles will always be equal, the one opposite the 72-degree one is also 72 degrees. Mark that one, too.

 

Since all 4 angles in a parallelogram must add up to 360 degrees, the remaining two have to add up to 360-72-72, which leaves you with 216.

 

So if those two add up to 216 and they are opposite and equal, each of those two must measure 108. Mark them.

 

Now you have all 4 angles of the parallelogram itself. Draw your criss-cross lines from each corner to the opposite corner, which creates Angle ZWY, which they tell you is 80 degrees. Since you know the big angle there is 108, subtract 108-80 to get the remaining angle (WYZ) of 28 degrees.

 

Remember, your sketch won't necessarily look "right," i.e. the proportions of the angle measurements might not make sense visually, but if you follow the rules about what you know about parallelograms, it will be correct.

 

AND, you can check your answers using what you know about triangles: all three angles in a triangle add to 90 degrees...

 

Hope this was clear/helpful!

 

Matt

Answer 2

opposite angles are congruent therefore angle WZY = 72 degrees

 

adjacent angles are supplementary therefore angle XWZ = 108 degrees

 

The sum of three angles in a triangle = 180 degrees, therefore angle WYZ = 180 - (80+72) = 180 - 152 = 28 degrees