Answer:
✒️CIRCLES
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\large\underline{\mathbb{ANSWERS}:}
ANSWERS:
\qquad \Large \:\: \rm a. \; m\angle EVO = 115\degreea.m∠EVO=115°
\qquad \Large \:\: \rm b. \; m\angle LOV = 86\degreeb.m∠LOV=86°
\qquad \Large \:\: \rm c. \; m\overset{\frown}{EVO} = 130\degreec.m
EVO
⌢
=130°
\qquad \Large \:\: \rm d. \; m\overset{\frown}{LOV} = 188\degreed.m
LOV
=188°
\large\underline{\mathbb{SOLUTION}:}
SOLUTION:
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
m\angle EVO + m\angle OLE = 180\degreem∠EVO+m∠OLE=180°
m\angle LOV + m\angle LEV = 180\degreem∠LOV+m∠LEV=180°
a. Find the measure of angle EVO
m\angle EVO + 65\degree = 180\degreem∠EVO+65°=180°
m\angle EVO = 180\degree- 65\degreem∠EVO=180°−65°
m\angle EVO = 115\degreem∠EVO=115°
b. Find the measure of angle LOV
m\angle LOV + 94\degree = 180\degreem∠LOV+94°=180°
m\angle LOV = 180\degree - 94\degreem∠LOV=180°−94°
m\angle LOV = 86\degreem∠LOV=86°
An the measure of an intercepted arc is twice the measure of the inscribed angle which intercepts it.
m\overset{\frown}{EVO} = 2(m\angle OLE)m
=2(m∠OLE)
m\overset{\frown}{LOV} = 2(m\angle LEV)m
=2(m∠LEV)
c. Find the measure of arc EVO
m\overset{\frown}{EVO} = 2(65\degree)m
=2(65°)
m\overset{\frown}{EVO} = 130\degreem
d. Find the measure of arc LOV
m\overset{\frown}{LOV} = 2(94\degree)m
=2(94°)
m\overset{\frown}{LOV} = 188\degreem
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Answers & Comments
Answer:
✒️CIRCLES
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\large\underline{\mathbb{ANSWERS}:}
ANSWERS:
\qquad \Large \:\: \rm a. \; m\angle EVO = 115\degreea.m∠EVO=115°
\qquad \Large \:\: \rm b. \; m\angle LOV = 86\degreeb.m∠LOV=86°
\qquad \Large \:\: \rm c. \; m\overset{\frown}{EVO} = 130\degreec.m
EVO
⌢
=130°
\qquad \Large \:\: \rm d. \; m\overset{\frown}{LOV} = 188\degreed.m
LOV
⌢
=188°
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\large\underline{\mathbb{SOLUTION}:}
SOLUTION:
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
m\angle EVO + m\angle OLE = 180\degreem∠EVO+m∠OLE=180°
m\angle LOV + m\angle LEV = 180\degreem∠LOV+m∠LEV=180°
a. Find the measure of angle EVO
m\angle EVO + m\angle OLE = 180\degreem∠EVO+m∠OLE=180°
m\angle EVO + 65\degree = 180\degreem∠EVO+65°=180°
m\angle EVO = 180\degree- 65\degreem∠EVO=180°−65°
m\angle EVO = 115\degreem∠EVO=115°
b. Find the measure of angle LOV
m\angle LOV + m\angle LEV = 180\degreem∠LOV+m∠LEV=180°
m\angle LOV + 94\degree = 180\degreem∠LOV+94°=180°
m\angle LOV = 180\degree - 94\degreem∠LOV=180°−94°
m\angle LOV = 86\degreem∠LOV=86°
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An the measure of an intercepted arc is twice the measure of the inscribed angle which intercepts it.
m\overset{\frown}{EVO} = 2(m\angle OLE)m
EVO
⌢
=2(m∠OLE)
m\overset{\frown}{LOV} = 2(m\angle LEV)m
LOV
⌢
=2(m∠LEV)
c. Find the measure of arc EVO
m\overset{\frown}{EVO} = 2(m\angle OLE)m
EVO
⌢
=2(m∠OLE)
m\overset{\frown}{EVO} = 2(65\degree)m
EVO
⌢
=2(65°)
m\overset{\frown}{EVO} = 130\degreem
EVO
⌢
=130°
d. Find the measure of arc LOV
m\overset{\frown}{LOV} = 2(m\angle LEV)m
LOV
⌢
=2(m∠LEV)
m\overset{\frown}{LOV} = 2(94\degree)m
LOV
⌢
=2(94°)
m\overset{\frown}{LOV} = 188\degreem
LOV
⌢
=188°
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