Explicație pas cu pas:
[tex]\angle IBC = \frac{\angle ABC}{2} \\ [/tex]
[tex]\angle ICB = \frac{\angle ACB}{2} \\ [/tex]
în ΔBIC:
[tex]\angle BIC = 180 - (\angle IBC + \angle ICB) \\ = 180 - \frac{\angle B + \angle C}{2} = 180 - \frac{180 - \angle A}{2} \\ = 180 - 90 + \frac{\angle A}{2} = 90 + \frac{\angle A}{2} \\ [/tex]
=>
[tex]140 = 90 + \frac{\angle A}{2} = > \frac{\angle A}{2} = 50 \\ [/tex]
[tex]\angle CAI = \frac{\angle A}{2} \\[/tex]
=> ∢CAI = 50°
