Question

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Answer 1

Step-by-step explanation:

EGF =FGH (Alternate interior angle)

FGH ,y= 40°

Y+Z = 70°(EXTERIOR ANGLE SUM PROPERTY)

40°+Z=70°

Z=70° -40°=30°

Answer 2

Answer:-

★ Given:

• EFGH is a parallelogram

• ∠EGF = 40°

• ∠FHA = 70°

• EF || GH

• GE || FH

★ To Find:

• Value of x = ∠FEG

• Value of y = ∠GFH

• Value of z = ∠FGH

★ Properties Used:

• Opposite Angles of a parallelogram are equal.

• Sum of adjacent Angles of a parallelogram is 180°.

• Alternate interior angles of the pair of parallel lines are equal.

• Sum of two angles in a straight line is 180°.

★ Solution:

➣ Finding the value of y

∠FGE = ∠GFH = y = 40°

[ Alternate interior Angles ]

➣ Finding the value of x

∠ FHG + ∠ FHA = 180° [By linear pair]

➟ ∠ FHG + 70° = 180°

➟ ∠ FHG = 180 - 70

∴ ∠ FHG = 110°

As we know opposite angles of a parallelogram are equal.

So,

∠ FHG = ∠ FEG = x = 110°

➣ Finding the value of z

∠ FEG + ∠ EGH = 180° [ Sum of adjacent angles ]

➟ ∠ x + (40° + z°) = 180°

➟ 110° + 40° + z° = 180°

➟ 150° + z° = 180°

➟ z° = 180° - 150°

∴ z = 30°

Value of x = 110°

Value of y = 40°

Value of z = 30°