Question

In ∆ ABC, ∠ABC  = 45°,  ∠BCA = 22.5° Find the ∠CAB in circular measure 
1. 5π/8
2. 3π/8
3. 4π/7
4. 6π/7

Answer 1

Correct Answer - Option 1 : 5π/8

Given:

In ∆ ABC,

∠ABC = 45°, ∠BCA = 22.5° 

Concept used: 

Radian measure = (π/180) × degree measure 

Sum of the angles of the triangle is 180° 

Calculation:

In ∆ ABC,

By angle sum property,

∠ABC + ∠BCA  + ∠CAB = 180°  

⇒ 45° + 22.5° + ∠CAB = 180° 

⇒ ∠CAB = 180°- 67.5° = 112.5° 

In circular measure,

∠CAB = 112.5 × (π/180)

⇒ ∠CAB = 5π/8 

∴ The ∠CAB in circular measure is 5π/8.