Question

Use the diagram and give information to match the angle measure with the angle

Answer 1

Given the triangle below:

It can be observed that

`m\angle ION=m\angle GOT(vertically\text{ opposite angles are equal)}`
`\begin{gathered} \text{if,m}\angle GOT=168^0,then \\ m\angle ION=m\angle GOT=168^0 \\ m\angle ION=168^0 \end{gathered}`

It can also be observed that

`\begin{gathered} m\angle AON+m\angle AOI=m\angle ION(given) \\ m\angle AOI=90^0(given,right-angle) \\ m\angle ION=168^0(derived\text{ earlier)} \\ So, \\ m\angle AON+90^0=168^0 \\ m\angle AON=168^0-90^0 \\ m\angle AON=78^0 \end{gathered}`

It can as well be observed that

`m\angle NOG=180^0(angle\text{ on a straight line)}`

Hence,

m∠ION = 168°

m∠AON = 78°

m∠NOG = 180°