Answer:
![arc(AD)=74\°](https://tex.z-dn.net/?f=arc%28AD%29%3D74%5C%C2%B0)
Step-by-step explanation:
Givens
- AC and BD are diameters.
- Angle BCA measures 53°.
Notice that line segment BE is congruent to line segment CE, because they are the radius of the circumference. That means the triangle that contains these sides is isosceles.
, by definition of triangles isosceles.
Then,
, by sum of internal angles.
And,
, by vertical angles definition.
![\angle DEA = 74\°](https://tex.z-dn.net/?f=%5Cangle%20DEA%20%3D%2074%5C%C2%B0)
But, we know that the measured of a subtended arc is equal to its angle.
Therefore, ![arc(AD)=74\°](https://tex.z-dn.net/?f=arc%28AD%29%3D74%5C%C2%B0)