Given CircleDot E with diameter BD find m angle ABD and mCDO

Given CircleDot E with diameter BD, find m angle ABD and mCD^OverParenthesis. m angle ABD _______ mCD^OverParenthesis = __________

Solution:

BD is diameter therefore angle subtended by 180

therefore arc subtended by arc AD = <ABD = 180 - arc AB = 180 - 116 = 64

<ABD = 64

for arc CD = angle subtended by <DBC in triangle DBC

m<DBC = 180 - <BDC - <DCB

= 180 - 58 -90

= 32

therefore arc DC = <DBC = 32

arc = 32