Question

Q7. ABCD is a parallelogram. Find x, y, z (3
Marks)Show the working on a sheet of
paper with complete steps and reasons in
the bracket
C с
D
Pr
45°
2
80°
B
A​

Answer 1

Given :

• ABCD is a parallelogram
• Angle DAC = 45°
• Exterior angle = 80°

To find :

• x , y and z

Solution :

exterior angle + angle ABC = 180° (Linear pair)

80° + angle ABC = 180°

angle ABC = 180° - 80°

angle ABC = 100°

$\because$ opposite angles of parallelogram are equal

x = angle ABC

• x = 100°

y = angle DAC (alternate interior angles)

• y = 45°

In ∆ADC

angle DAC + angle DCA + angle CDA = 180° (angle sum property of a triangle)

45° + angle DCA + 100° = 180°

145° + angle DCA = 180°

angle DCA = 180° - 145°

angle DCA = 35°

z = angle DCA (alternate interior angles)

• z = 35°

Therefore , the values of x , y and z respectively are 100° , 45° and 35° .

Answer 2

Answer:

Given :

• ABCD is a parallelogram

• ∠DAC = 45°

• Exterior angle = 80°

To find :

• The value of x , y and z

Solution :

exterior angle + angle ABC = 180° (Linear pair)

=>80° + ∠ABC = 180°

=>∠ABC = 180° - 80°

=>∠ABC = 100°

•  opposite angles of parallelogram are equal

=>x = angle ABC

=>x = 100°

=>y = ∠DAC [alternate interior angles]

=>y = 45°

In ∆ADC

• ∠ DAC + ∠DCA + ∠CDA = 180° [angle sum property of a triangle]

=>45° + ∠DCA + 100° = 180°

=>145° + ∠DCA = 180°

=>∠DCA = 180° - 145°

=>∠DCA = 35°

=>z = ∠DCA [alternate interior angles]

z = 35°

Therefore the values of:-

• x = 100°
• y = 45°
• z= 35°