Respuesta :

AJRL2005

Answer:

x = 55

y = 60

Step-by-step explanation:

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. So E and G are supplementary, and H and F are supplementary.

x + 15 + 2x = 180

3x + 15 = 180          combine like terms

3x = 165                  subtract 15 from both sides

x = 55                       divide both sides by 3

y + 3y - 60 = 180

4y - 60 = 180           combine like terms

4y = 240                  subtract 60 from both sides

y = 60                      divide both sides by 4

Answer:

Step-by-step explanation:

For inscribed quadrilateral, each opposite interior angle pair is supplementary.

m<HEF + m<HGF = 180

x + 15 + 2x = 180

3x = 165

x = 55

m<GHE + m<GFE = 180

y + 3y - 60 = 180

4y = 240

y = 60

<EHG = y = 60deg.

<HGF = 2x = 110deg.

<GFE = 3y - 60 = 120deg.

<FEH = x + 15 =70deg.

m arc HF = m<center angle HJF

= 2 x m<FEH = 2 x 70

= 140

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