Question

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

Answer 1

Answer:

26 degrees.

Step-by-step 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

$\angle HIG=\dfrac{\angle GOH}{2}$

$\angle HIG=\dfrac{52^{\circ}}{2}$

$\angle HIG=26^{\circ}$

Therefore, the measure of angle HIG is 26 degrees.