The quadrilateral ABCD is inscribed in a circle. The ABC angle is 140 degrees, the CAD angle is 84 degrees.
| May 22, 2021 | education
The quadrilateral ABCD is inscribed in a circle. The ABC angle is 140 degrees, the CAD angle is 84 degrees. Find the angle ABD.
Before solving the problem, it is necessary to make a drawing and apply known data.
Consider angle ABC: angle ABC consists of two parts – angle ABD and angle CBD.
Hence, the angle ABD is equal to the difference between the angle ABC and the angle CBD.
The CAD inscribed corner rests on the CD arc, the CBD inscribed corner also rests on the CD arc. Therefore, the inscribed CAD and CBD angles are equal: CAD = CBD = 84 °.
This means that the angle ABD = ABC – CBD = 140 ° – 84 ° = 56 °.
Answer: The degree measure of the ABD angle is 56 °.
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.
