Question

Find the values of unknown variables x , y , z in the following parallelogram.

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Answer 1

(i) x+100=180 [Adjacent angles]

(i) x+100=180 [Adjacent angles]x=80

(i) x+100=180 [Adjacent angles]x=80z=x=80

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130 and z=x=130

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130 and z=x=130 (corresponding angles)

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130 and z=x=130 (corresponding angles)(iii) x=90

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130 and z=x=130 (corresponding angles)(iii) x=90 (vertically opposite angles)

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130 and z=x=130 (corresponding angles)(iii) x=90 (vertically opposite angles)x+y+30=180

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130 and z=x=130 (corresponding angles)(iii) x=90 (vertically opposite angles)x+y+30=180

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130 and z=x=130 (corresponding angles)(iii) x=90 (vertically opposite angles)x+y+30=180 y=180−120=60

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=130 x=y=130 and z=x=130 (corresponding angles)(iii) x=90 (vertically opposite angles)x+y+30=180 y=180−120=60

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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)

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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)

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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)

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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

(i) x+100=180 [Adjacent angles]x=80z=x=80 [opposite angles are equal]y=100 (ii) 50+y=180y=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 pro.perty)

perty)x=180−152

perty)x=180−152x=28

z=x=28

z=x=28 (Alter.nate angl.es)