Multiple choice

ED is chord parallel to the diameter AC of a circle. A point B is on the perimeter of the circle such that angle $CBE= 63^{\circ}$. The angle DEC is equal to

  1. $63^{\circ}$
  2. $42^{\circ}$
  3. $31.5^{\circ}$
  4. $27^{\circ}$
Reveal answer Fill a bubble to check yourself
D Correct answer
AI explanation

Since ED is parallel to the diameter AC, the alternate angles CED and ECA are equal. Because AC is the diameter, angle ABC is 90 degrees, making angle ECA equal to 90 degrees minus angle CBE. Substituting the given value of angle CBE as 63 degrees, we find angle ECA equals 90 degrees minus 63 degrees, which is 27 degrees. Therefore, angle DEC is equal to 27 degrees.