In ΔABC, ∠A + ∠B = 70° and ∠B + ∠C = 135°. Find the measure of each angle of the triangle.

Given ∠A + ∠B = 70° and ∠B + ∠C = 135°

We know that sum of the angles of a triangle is 180°.

∠A + ∠B + ∠C = 180° …I

Also, ∠A + ∠B + ∠B + ∠C = 70° + 135°

⇒ (∠A + ∠B + ∠C) + ∠B = 205°

From I,

⇒ 180° + ∠B = 205°

⇒ ∠B = 205° - 180°

⇒ ∠B = 25°

Putting in given equations,

∠A + ∠B = 70° and ∠B + ∠C = 135°

⇒ ∠A + 25° = 70° and 25° + ∠C = 135°

⇒ ∠A = 45° and ∠C = 110°

So, the angles of the triangle are 45°, 25° and 110°.