AC and BD are chords of one circle, and E is the point of their intersection.
| August 30, 2021 | education
AC and BD are chords of one circle, and E is the point of their intersection. The CED is 9 times the BEC and the DAE is 61 degrees the BEC. Find the angle CBE
Let the value of the angle BEC = X0, then, according to the condition, the angle CED = 9 * X0.
The angles BEC and CED are adjacent angles, the sum of which is 180. Then the angle BEC + CED = 180.
X + 9 * X = 180.
10 * X = 180.
X = BCE = 180/10 = 180.
Angle CED = 18 * 9 = 162.
Since the angle DАЕ is 61 more than the angle BEC, then the angle DАЕ = 62 + 18 = 80.
The angle DАЕ is equal to the inscribed angle DАС, which rests on the arc СD. Since the angle СBЕ = СBD, and the inscribed angle СBD rests on the arc СD, then the angle СBЕ = DАЕ = 80.
Answer: The CBE angle is 80.
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