Question

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

Answer 1

Answer:

$m(\widehat{EH})$ = 130°

Step-by-step 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, $m(\widehat{HG})=(3\times 20) - 10$

                               = 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°