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# In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size ...

### Question

In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size of <EHF.

A) 126o

B) 72o

C) 64cmo

D) 32cmo

### Explanation:

F = 54$$^{\circ}$$ (Alternate triangle angles)
< GHE = F = 54$$^{\circ}$$(Angle between a chord and a tangent = angles in the alternate segment)
Now, < GHE + < EHF + < IHF = 180$$^{\circ}$$(Angles on a straight line)
54$$^{\circ}$$ + < EHF + 54$$^{\circ}$$= 180$$^{\circ}$$
< EHF = 180$$^{\circ}$$- 108$$^{\circ}$$
= 72$$^{\circ}$$

## Dicussion (1)

• F = 54$$^{\circ}$$ (Alternate triangle angles)
< GHE = F = 54$$^{\circ}$$(Angle between a chord and a tangent = angles in the alternate segment)
Now, < GHE + < EHF + < IHF = 180$$^{\circ}$$(Angles on a straight line)
54$$^{\circ}$$ + < EHF + 54$$^{\circ}$$= 180$$^{\circ}$$
< EHF = 180$$^{\circ}$$- 108$$^{\circ}$$
= 72$$^{\circ}$$