a) Ta có:
\(\widehat{xOy} + \widehat{yOz} = 180^O\) (kề bù)
\(70^O + \widehat{yOz} = 180^O (\widehat{xOy} = 70^O(gt))\)
\(\widehat{yOz} = 180^O - 70^O\)
\(\widehat{yOz} = 110^O\)
Vậy \(\widehat{yOz} = 110^O\)
b) Ta có:
\(\widehat{aOy} = \frac{\widehat{xOy}}{2}\) (Oa là tia phân giác của \(\widehat{xOy}\)(gt))
\(\widehat{aOy} = \frac{70^O}{2} (\widehat{xOy} = 70^O(gt))\)
\(\Rightarrow\)\(\widehat{aOy} = 35^O\)
\(\widehat{aOy} + \widehat{yOz} = \widehat{aOz}\) (Oy nằm giữa hai tia Oa và Oz)
\(35^O + 110^O = \widehat{aOz} (\widehat{aOy}=35^O (cmt); \widehat{yOz} = 110^O (cmt))\)
\(\Rightarrow\)\(\widehat{aOz} = 145^O\)
Vậy \(\widehat{aOz} = 145^O\)
c) Ta có:
\(\widehat{yOb} = \frac{\widehat{yOz}}{2}\) (Ob là tia phân giác của \(\widehat{yOz}\)(gt))
\(\widehat{yOb} = \frac{110^O}{2} (\widehat{yOz} = 110^O(cmt))\)
\(\Rightarrow\)\(\widehat{yOb} = 55^O\)
\(\widehat{yOb} + \widehat{aOy} = \widehat{aOb}\) (Oy nằm giữa Oa và Ob)
\(55^O + 35^O = \widehat{aOb}(\widehat{yOb}=55^O (cmt); \widehat{aOy} = 35^O (cmt))\)
\(\Rightarrow\)\(\widehat{aOb} = 90^O\)
Vậy \(\widehat{aOb} = 90^O\)