Question

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Answer 1

1.

Given,

CBX = 64°

CBA + CBX = 180°

⇒ CBA + 64° = 180°

⇒ CBA = 180° - 64°

⇒ CBA = 116°.

Since , ABCD is a parallelogram , so opposite angle will be equal.

∴  CBA = ADC

⇒ 116° = y.

Now,

Sum of adjacent angles = 180°

⇒CBA + DAB = 180°

⇒ 116° + z = 180°

⇒ z = 180° - 116°

∴ z = 64°= DAB

And,

⇒ DAB = BCD

∴ 64° = x.

X = 64 , Y = 116 and Z = 64.

      ________________________________________________

4. Since the figure in this question is rhombus.

So, adjacent sides will be equal.

⇒ 13 cm = ( y + 4 ) cm

⇒ 13 cm = y cm + 4 cm

⇒ y cm = 13 cm - 4cm

⇒ y cm = 9 cm

⇒ y = 9 cm / cm

∴ y = 9.

And, sum of adjacent angles = 180°.

⇒ 75° + x = 180°

⇒ x = 180° - 75°

∴ x = 105°.

Now,

Opposite angles will be also equal.

⇒ x = z

∴ z = 105°.

So, x = z = 105 and y = 9.

                 _______________________________

6. Refer to the attachment for clear explanation of points.

Since the given figure is a square.

∴ Diagonals will bisect each other at  90°.

 ∴  z = 90°.

Adjacent sides of a square is equal.

 AB = BC 

∴ BAC = ACB

 ∴ x = y

In triangle ABC ,

 BAC + ABC + ACB = 180°

⇒ x + y + 90° = 180°

 ⇒ x + x = 180° - 90°

⇒ 2x = 90°

⇒ x = 90° / 2

∴ x = 45° = y.

So, x = y = 45 and z = 90.

      _______________________________________________

12.b . Refer to the attachment for explanation of points.


We know that all angles of a rectangle is of 90°.

In Δ ABD,

 ⇒ ABD + ADB + BAD = 180°

 ⇒ x + y + 90° = 180°


 ⇒ x + y = 180° - 90°

 ∴ x + y = 90°

Given , 

 x : y = 2 : 7.

Let z in included in the ratio.

 ∴ x = 2z and y = 7z.

Now,

⇒ x + y = 90°

⇒ 2z + 7z = 90°

⇒ 9z = 90°

⇒ z = 90° / 9

∴ z = 10°.

So,

 x = 2z = 2 × 10° = 20°

 y = 7z = 7 × 10° = 70°.

 

Answer 2

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