Question

In the circle below, O is the center and mĞ= 128° What is the measure of angle HIG?​

Answer 1

26 degrees.

Explanation:

From the figure it is clear that HI is the diameter and
`acr(GI)=128^(\circ)`. So,

`\angle GOI=128^(\circ)`

`\angle GOI+\angle GOH=180^(\circ)` (linear pair)

`128^(\circ)+\angle GOH=180^(\circ)`

`\angle GOH=180^(\circ)-128^(\circ)`

`\angle GOH=52^(\circ)`

Using central angle theorem of a circle, we get

`\angle HIG=(\angle GOH)/(2)`

`\angle HIG=(52^(\circ))/(2)`

`\angle HIG=26^(\circ)`

Therefore, the measure of angle HIG is 26 degrees.