Question

5. In the given quadrilateral ABCD (not drawn to scale), BC = AC = AD. AD is a diangonal and angle ABC=62* and angle ADC=52*. Find the sum of angle DAC
and angle ACB.
(a) 76°
(b) 132
(c) 56°
(d) 112​

Answer 1

Answer:

In given figure,

Quadrilateral ABCD is a parallelogram.

So, AD ∣∣ BC

∴ ∠DAC = ∠ACB --- ( Alternate angle)

∴ ∠ACB = 32

∘

∠AOB + ∠BOC = 180

∘

--- (straight angle)

⇒70

∘

+ ∠BOC = 180

∘

∴ ∠BOC = 110

∘

In △BOC,

∠OBC + ∠BOC + ∠OCB = 180

∘

⇒∠OBC + 110

∘

+ 32

∘

= 180

∘

⇒ ∠OBC = 38

∘

∴ ∠DBC = 38

∘