1.)
(x + 138) + (x + 48) = 180
x + 138 + x + 48 = 180
2x + 186 = 180
2x = 180 - 186
2x = -6
x = -3
mKG = x + 138
mKG = (-3) + 138
mKG = 135° (A)
2.)
(Since angle FEG is a central angle, its arc value is its angle value)
(Since line FE passes through the center, it is a diameter which divides the angle value of the circle into two resulting to 180 degrees)
m∠GEH = 180 - 64
m∠GEH = 116° (B)
3.)
Apply intersecting chords theorem
m∠x = (arcCD + arcBA)
m∠x = (80 + 230)
m∠x = (310)
m∠x = 155° (C)
4.)
Apply tangent - tangent theorem
m∠x = (majorarcBA- minorarcBA)
m∠x = (200- 160)
m∠x = (40)
m∠x = 20° (C)
5.)
Apply the relationship between central angle and inscribed angle
let x be the inscribed angle
let y be the central angle
x = y
x = (90)
x = 45° (A)
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Verified answer
1.)
(x + 138) + (x + 48) = 180
x + 138 + x + 48 = 180
2x + 186 = 180
2x = 180 - 186
2x = -6
x = -3
mKG = x + 138
mKG = (-3) + 138
mKG = 135° (A)
2.)
(Since angle FEG is a central angle, its arc value is its angle value)
(Since line FE passes through the center, it is a diameter which divides the angle value of the circle into two resulting to 180 degrees)
m∠GEH = 180 - 64
m∠GEH = 116° (B)
3.)
Apply intersecting chords theorem
m∠x = (arcCD + arcBA)
m∠x = (80 + 230)
m∠x = (310)
m∠x = 155° (C)
4.)
Apply tangent - tangent theorem
m∠x = (majorarcBA- minorarcBA)
m∠x = (200- 160)
m∠x = (40)
m∠x = 20° (C)
5.)
Apply the relationship between central angle and inscribed angle
let x be the inscribed angle
let y be the central angle
x = y
x = (90)
x = 45° (A)