Question

In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB = 

A. 70° 

B. 45° 

C. 50° 

D. 60°

Answer 1

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°