Question

Abcd is a quadrilateral whose diagonals intersect each other at the point o such that oa = ob = od. If ∠oab = 50^{\circ}, then find the measures of ∠oda.

Answer 1

Given:

Abcd is a quadrilateral whose diagonals intersect each other at the point o such that oa = ob = od.  

To find:

If ∠oab = 50^{\circ}, then find the measures of ∠oda.

Solution:

From given, we have,

∠ oab = 50°

we have,

∠ oab = ∠ oba = 50°

In Δ AOB,

∠ oab + ∠ oba + ∠ aob = 180°

∠ aob = 180° - (50° + 50°)

∴ ∠ aob = 80°

In Δ OAD,

∠ oad + ∠ oda + ∠ aod = 180°

x + x + 100° = 180°

2x = 80°

x = 40°

∴ ∠ oda  = 40°