Question

Two line segments ${\displaystyle \overline{\text{AD}}}$ and ${\displaystyle \overline{\text{BC}}}$ intersect at O. Joining ${\displaystyle \overline{\text{AB}}}$ and ${\displaystyle \overline{\text{DC}}}$ we get two triangles, ∆AOB and ∆DOC as shown in the figure. Find the ∠A and ∠B

Answer 1

In ∆AOB and ∆DOC,

∠AOB = ∠DOC   ...[∵ Vertically opposite angles are equal]

Let ∠AOB = ∠DOC = y

By angle sum property of a triangle we have

∠A + ∠B + ∠AOB = ∠D + ∠C + ∠DOC = 180°

3x + 2x + y = 70° + 30° + y = 180°

5x + y = 100° + y = 180°

Here 5x + y = 100° + y

5x = 100° + y – y

5x = 100°

x = ${\displaystyle \frac{{100}^{\circ }}{5}}$ = 20°

∠A = 3x = 3 × 20 = 60°

∠B = 2x = 2 × 20 = 40°

∠A = 60°

∠B = 40°