In the given figure, HEFG is a parallelogram. Find the values of x, y and z.
H
G
110°
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Step-by-step explanation:
∵EFGH is a parallelogram.
⇒ ∠FGH+∠FGK=180
o
[ Linear pair ]
⇒ ∠FGH+70
o
=180
0
∴ ∠FGH=110
o
⇒ ∠FGH=∠FEH=110
o
[ Opposite angles of a parallelogram are equal ]
∴ x=110
o
Now, ∠EHG+∠FGH=180
o
[ Sum of adjacent angles of parallelogram is 180
o
. ]
⇒ ∠EHF+∠FHG+∠FGH=180
o
⇒ 40
o
+z+110
o
=180
o
⇒ z+150
o
=180
o
∴ z=30
o
⇒ ∠EHG=40
o
+z
=40
o
+30
o
⇒∠EHG=70
o
⇒ ∠FHG+∠HGF+∠GFH=180
o
[ Sum of angles of triangle is 180
o
]
⇒ 30
o
+110
o
+y=180
o
⇒ 140
o
+y=180
o
∴ y=40
o
We get, x=110
o
,y=40
o
,z=30
o
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