Two Inscribed Angles with the Same Arc

An important consequence of this is:

Theorem 4:  If two inscribed angles incept the same arc, then they are congruent.

Since angles ABD and ACD both intercept arc AD each measures half that arc, so they have the same measure and are therefore congruent.

Example 3:  What is the measure of arc ABC?

Solution:  Since angle ADC is an inscribed angle, it is half its intercepted arc.  Therefore the measure of that arc is twice this angle, or 160^o.

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