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8. In the given figure, O is the centre of the circle andAB is the diameter of the circle. If difference ofangle COD and angle DBC is 25°, then find the measure of angle DEB |
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Answer» In the figure given below, O is the CENTER of the circle. Chord CD is parallel to diameter AB. If angle ABC = 35 degrees, how would you calculate the angle CED?∠BCD = ∠ABC (alternate ∠s in AB//CD) . . . so ∠BCD = 35°∠OCB = ∠OBC (BASE ∠s of isosceles ∆OCB) . . . so ∠OCB = 35°∠OCD = ∠OBC + ∠BCD = 35° + 35° . . . so ∠OCD= 70°∠ODC = ∠OCD (base ∠s of isosceles ∆OCD) . . . so ∠ODC = 70°∠COD = 180° - ∠OCD - ∠ODC (sum of INTERIOR ∠s of ∆OCD) = 180° - 70° - 70° = 40° . . . so ∠COD = 40°Finally, ∠CED = ∠COD2 (∠ at circumference = half ∠ at centre)So ∠CED = 40°2=20°Step-by-step explanation:HOPE it helps |
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