Answer:
Correct option: A
Step-by-step explanation:
The angle BDC inscribe the arc mBC, so we have that:
mBDC = (1/2) * mBC
mBDC = (1/2) * 118 = 59°
From the secants relation in a circle, we have that:
mA = (1/2) * (mBC - mDE)
35 = (1/2) * (118 - mDE)
70 = 118 - mDE
mDE = 48°
The sum of the arcs is 360°, so we have:
mBC + mCD + mDE + mBE = 360
118 + mCD + 48 + 76 = 360
mCD = 360 - 118 - 48 - 76 = 118°
The angle mCBD inscribes the arc mCD, so we have:
mCBD = (1/2) * mCD = (1/2) * 118 = 59°
The angles mCBD and mBDC are equal, so the triangle is isosceles.
Correct option: A
