Answer:
[tex]m(\widehat{EH})[/tex] = 130°
Step-by-step explanation:
Angles subtended at the center by the arcs [tex](\widehat{HG})[/tex] and [tex](\widehat{EF})[/tex] are ∠HPG and ∠EPF.
Since these angles are the vertical angles both will be equal.
m∠HPG ≅ m∠EPF
3x - 10 = 2x + 10
3x - 2x = 10 + 10
x = 20
Therefore, [tex]m(\widehat{HG})=(3\times 20) - 10[/tex]
= 50°
Similarly [tex]m(\widehat{EF})[/tex] = 50°
In the same way angles subtended at the center will be equal.
m∠EPH ≅ m∠FPG
and [tex]m(\widehat{EH})=m(\widehat{FG})[/tex]
Since [tex]m(\widehat{EH})+m(\widehat{FG})+m(\widehat{EF})+m(\widehat{HG})=360[/tex]°
[tex]m(\widehat{EH})+m(\widehat{EH})+50+50=360[/tex]
[tex]2m(\widehat{EH})=360-100[/tex]
[tex]m(\widehat{EH})=130[/tex]
Therefore, measure of arc EH = 130°
