Quadrilateral ABCD is inscribed in a circle, K is the intersection point of the diagonals of the quadrilateral
| July 20, 2021 | education
Quadrilateral ABCD is inscribed in a circle, K is the intersection point of the diagonals of the quadrilateral, Find the angle BAC, if angle ACD = 74, angle AKD = 132.
Angles AKB and AKD are adjacent angles, the sum of which is 180, then the angle AKB = (180 – AKD) = (180 – 132) = 58.
The inscribed angle ACD rests on the arc AD, then the degree measure of the arc AD = 2 * 74 = 148.
The inscribed angle ABD also rests on the arc AD, then the inscribed head ABD = 148/2 = 74.
In the triangle ABK, the angle BAK = (180 – ABK – AKB) = (180 – 74 – 58) = 48.
Angle ABC = ABK = 48.
Answer: Angle ABC is 48.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
