Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
|
No Answers Yet
Help Sreelatha! Anyone can contribute an answer, even non-tutors.
can we consider AFEB as a quadrilateral having sum 360. if so how to get A
Date Posted: 3 years ago
Views: 430
Any quadrilateral has an angle sum of 360°.
AFE = 90°
(tangent is perpendicular to radius/diameter)
Since we have a regular octagon, and angle sum of polygon = (n-2) x 180°, where n is the number of sides,
Every interior angle of the octagon is identical in measure
(8 - 2) x 180°
= 1080°
1080° ÷ 8 = 135°
so ∠ABC = 135° since it's one of the interior angles.
(tangent is perpendicular to radius/diameter)
Since we have a regular octagon, and angle sum of polygon = (n-2) x 180°, where n is the number of sides,
Every interior angle of the octagon is identical in measure
(8 - 2) x 180°
= 1080°
1080° ÷ 8 = 135°
so ∠ABC = 135° since it's one of the interior angles.
OAB and OBC are congruent isosceles triangles
(SSS congruency.
OA = OB = OC = radius of circle.
OB is common.
AB = BC since they are identical sides of a regular octagon)
So ∠OBA = ∠OBC = ∠OAB = ∠OCB
Since ∠ABC= ∠OBA + ∠OBC,
∠ABC = 2∠OBA
∠OBA = ½∠ABC
= 135° ÷ 2
= 67.5°
(SSS congruency.
OA = OB = OC = radius of circle.
OB is common.
AB = BC since they are identical sides of a regular octagon)
So ∠OBA = ∠OBC = ∠OAB = ∠OCB
Since ∠ABC= ∠OBA + ∠OBC,
∠ABC = 2∠OBA
∠OBA = ½∠ABC
= 135° ÷ 2
= 67.5°
So ∠OAB is also 67.5°
∠FEB
= angle sum of quadrilateral AFEB - ∠AFE - ∠OAB - ∠ABC
= 360° - 90° - 67.5° - 135°
= 67.5°
∠FEB
= angle sum of quadrilateral AFEB - ∠AFE - ∠OAB - ∠ABC
= 360° - 90° - 67.5° - 135°
= 67.5°
360 Tutoring Program