The measure of m∠BDC is 68.
What is arc?
An arc of a circle is any portion of the circumference of a circle. To recall, the circumference of a circle is the perimeter or distance around a circle. Therefore, we can say that the circumference of a circle is the full arc of the circle itself.
Minor And Major Arc:
An arc less than one-half of the whole arc of the circle is called the minor arc of the circle, and an arc greater than one-half of the whole arc is called the major arc of the circle.
Axiom of Equal Arcs: If two arcs subtend equal angles at the centres or centre in equal circles or the same circle, they are equal.
- In equal circles or the same circle, equal chords cut off equal arcs.
- In equal circles or the same circle, if two arcs are equal, then their chords are equal.
Given:
mAC 178°, mBC= 42
Now, using
angle= far arc- near arc /2
m∠BDC = 1/2(178 - 42)
m∠BDC = 1/2(136)
m∠BDC = 68
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