Question

3. Find the values of unknowns x, y, z, if ABCD is a parallelogram. (a) (b) (C) VY D С C A B E B F il 7 75017 60° X 70° X ED С C. A B HD​

Answer 1

Answer:

(i) x+100=180 [Adjacent angles]

x=80

z=x=80∘ [opposite angles are equal]

y=100∘

(ii) 50+y=180

y=130∘

x=y=130∘ and z=x=130∘ (corresponding angles)

(iii) x=90∘ (vertically opposite angles)

x+y+30=180∘

y=180−120=60∘

z=y=60∘ (Alternate angles)

(iv) z=80,y=80 (Opposite angles)

x+y=180∘,x=180−80⇒x=100∘

(v) y=112∘ (opposite angles)

x+y+40=180∘ (Angle sum property)

x=180−152

x=28∘

z=x=28∘ (Alternate angles)