Question

Select the correct answer from each drop-down menu. For circle O, and m∠ABC = 55°. In the figure, ∠ and ∠ have measures equal to 35°.

Answer 1

Answer:

CA is a diameter of the circle, so m\widehat{AC}=180^\circmAC=180∘ , which means m\angle AOB=m\angle AOD=m\widehat{AD}=180^\circ-m\widehat{CD}=55^\circm∠AOB=m∠AOD=mAD=180∘−mCD=55∘ . Then m\boxed{\angle ABO}=90^\circ-55^\circ=35^\circm∠ABO=90∘−55∘=35∘ .

This means m\angle CBO=55^\circ-35^\circ=20^\circm∠CBO=55∘−35∘=20∘ . Also, if m\angle AOB=55^\circm∠AOB=55∘ , then m\angle BOC=180^\circ-55^\circ=125^\circm∠BOC=180∘−55∘=125∘ , which in turns tells us that m\boxed{\angle BCO}=180^\circ-20^\circ-125^\circ=35^\circm∠BCO=180∘−20∘−125∘=35∘ .