Question

Calculate the angles of the quadrilateral shown in the fig.

Answer 1

∠ACB and ∠ADB are the angles subtended by an arc AB in the same segment.
So, ∠ACB = ∠ADB
∠ACB = 30°

∠ACD and ∠ARD are the angles subtended by an arc AD in the same segment.
So ∠ACD = ∠ABD

∠ABD = 45°
∠CAD and ∠CBD are the angles subtended by an arc CD in the same segment.

So, ∠CAD = ∠CBD
∠CBD = 50°

Now,
∠C = ∠ACD + ∠ACB
= 45° + 30° = 75°

∠A + ∠C = 180°
∠A = 180° - 75° = 105°

∠B = ∠ABD +∠CBD
= 45° + 50° = 95°

∠B+∠D =180°
∠D = 180° - 95° = 85°