Question

In circle P, EG and FH are diameters.
What is m EH?

Answer 1

`m(\widehat{EH})` = 130°

Explanation:

Angles subtended at the center by the arcs
`(\widehat{HG})` and
`(\widehat{EF})` 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,
`m(\widehat{HG})=(3* 20) - 10`

= 50°

Similarly
`m(\widehat{EF})` = 50°

In the same way angles subtended at the center will be equal.

m∠EPH ≅ m∠FPG

and
`m(\widehat{EH})=m(\widehat{FG})`

Since
`m(\widehat{EH})+m(\widehat{FG})+m(\widehat{EF})+m(\widehat{HG})=360`°

`m(\widehat{EH})+m(\widehat{EH})+50+50=360`

`2m(\widehat{EH})=360-100`

`m(\widehat{EH})=130`

Therefore, measure of arc EH = 130°