Question

The figure HOPE is a parallelogram. Find the angle measure x,y, and z. State the properties you use to find the.

Answer 1

i)Angle y=40°. (alternate int. angles.)
 Let angle POH be angle 1
 angle 1+70° =180°  (Linear pair)
 angle 1=180-70=110°
 Angle 1+y+z=180°  (Angle Sum Property of Triangle)
 110 +40+z=180
 150+z=180
 z=180-150=30°
iii) 40+z+x=180  (co-interior angles)
   40+30+x=180
   70+x=180
    x=180-70=110°


therefore x=110,y=40,z=30

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Answer 2

angle o inside parallelogram = 180-70=110 degree(supplementary angles)

angle x=angle o=110 degree (opposite angle of ||gm are equal)

angle y =40 degree (alternate interior angles are equal)

angle H= 70 degree (corresponding angles are equal)

Angle H=40 degree + angle z=70 degree

angle z= 70 degree - 40 degree

angle z =30 degree

angle x =110
angle y =40
angle z=30 degree