Question

In the adjoining figure, ABCD is a parallelogram in which ∠BAO = 35°, ∠DAO = 40° and ∠COD = 105°. Calculate (i) ∠ABO, (ii) ∠ODC, (iii) ∠ACB, (iv) ∠CBD.

Answer 1

ABCD is a parallelogram.
∴ AB ∣∣​ DC and BC ​∣∣​ AD

(i) In ∆AOB, ∠BAO = 35°, ​∠AOB = ∠COD = 105° (Vertically opposite angels)
∴ ​∠ABO = 180^o − (35^o + 105^o) = 40^o

(ii)∠ODC and ∠ABO are alternate interior angles.
∴ ∠ODC = ∠ABO = 40^o

(iii) ∠ACB = ∠​CAD = 40^o (Alternate interior angles)

(iv) ∠CBD = ∠ABC − ∠ABD ...(i)

∠ABC = 180^o − ∠BAD (Adjacent angles are supplementary) ​

​⇒∠ABC = 180^o − 75^o = 105^o
⇒∠CBD = 105^o − ∠ABD (∠ABD = ∠ABO)
⇒∠CBD = 105^o − 40^o = 65^o