In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB = A. 70° B. 45°

1.	In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB = A. 70° B. 45° C. 50° D. 60°
Answer» Option : (C) The diagonals in a rhombus are perpendicular, So, ∠BPC = 90° From triangle BPC, The sum of angles is 180° So, ∠CBP = 180° – 40° – 90° = 50° Since, triangle ABC is isosceles We have, AB = BC So, ∠ACB = ∠CAB = 40° Again from triangle APB, ∠PBA = 180° – 40° – 90° = 50° Again, triangle ADB is isosceles, So, ∠ADB = ∠DBA = 50° ∠ADB = 50°

In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB = A. 70° B. 45° C. 50° D. 60°

Answer»

Option : (C)

The diagonals in a rhombus are perpendicular,

So,

∠BPC = 90°

From triangle BPC,

The sum of angles is 180°

So,

∠CBP = 180° – 40° – 90°

= 50°

Since, triangle ABC is isosceles

We have,

AB = BC

So,

∠ACB = ∠CAB = 40°

Again from triangle APB,

∠PBA = 180° – 40° – 90° = 50°

Again, triangle ADB is isosceles,

So,

∠ADB = ∠DBA = 50°

∠ADB = 50°