Question

UNDERSTANDING QUADRILATERALS 151
2. Consider the following parallelograms. Find the values of the unknowns x, y, z.
D
y
C
x
A
z
B
100°
A
B
Z
(i)
y
у
30°
400
1120
80
Z
(iv)
(V)
1​

Answer 1

Step-by-step explanation:

(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)

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Answer 2

Answer:

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