Question

what is the relation between an inscribed angle and the arc intercepted by it​

Answer 1

Answer:

ᴛʜᴇ ᴠᴇʀᴛᴇx ᴏғ ᴀɴ ɪɴsᴄʀɪʙᴇᴅ ᴀɴɢʟᴇ ᴄᴀɴ ʙᴇ ᴀɴʏᴡʜᴇʀᴇ ᴏɴ ᴛʜᴇ ᴄɪʀᴄʟᴇ ᴀs ʟᴏɴɢ ᴀs ɪᴛs sɪᴅᴇs ɪɴᴛᴇʀsᴇᴄᴛ ᴛʜᴇ ᴄɪʀᴄʟᴇ ᴛᴏ ғᴏʀᴍ ᴀɴ ɪɴᴛᴇʀᴄᴇᴘᴛᴇᴅ ᴀʀᴄ. ᴛʜᴇ ɪɴsᴄʀɪʙᴇᴅ ᴀɴɢʟᴇ ᴛʜᴇᴏʀᴇᴍ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴛʜᴇ ᴍᴇᴀsᴜʀᴇ ᴏғ ᴀɴ ɪɴsᴄʀɪʙᴇᴅ ᴀɴɢʟᴇ ɪs ʜᴀʟғ ᴛʜᴇ ᴍᴇᴀsᴜʀᴇ ᴏғ ɪᴛs ɪɴᴛᴇʀᴄᴇᴘᴛᴇᴅ ᴀʀᴄ. ɪɴsᴄʀɪʙᴇᴅ ᴀɴɢʟᴇs ᴛʜᴀᴛ ɪɴᴛᴇʀᴄᴇᴘᴛ ᴛʜᴇ sᴀᴍᴇ ᴀʀᴄ ᴀʀᴇ ᴄᴏɴɢʀᴜᴇɴᴛ.

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Answer 2

Answer:

We define the arc angle to be the measure of the central angle which intercepts it. The Inscribed Angle Conjecture I gives the relationship between the measures of an inscribed angle and the intercepted arc angle. It says that the measure of the intercepted arc is twice that of the inscribed angle.