the measure of are RC is 120 degrees.
The know the measure of arc RC, we need to know the type of the angle.
What are the types of a triangle?
Types of triangle-
- Scalene triangle- When all the sides of a triangle are unequal, then the triangle is known as scalene triangle.
- Isosceles triangle- When all two sides and two angles of a triangle are equal, then the triangle is known as isosceles triangle.
- Equilateral triangle- When all the three sides and all the three angle of a triangle are equal, then the triangle is known as Equilateral triangle.
In the given problem all the sides of the triangle is equal. Thus it is an equilateral triangle. Thus all the sides of the triangle should be equal.
Hence,
[tex]AC=CR=AR[/tex]
[tex]\angle ACR=\angle ARC=\angle CAR[/tex]
As all the sides are equal and angle are equal in length, thus each section has equal arc measure.
For a circle the sum of all the sides are equal to 360 degrees thus arc of RC is,
[tex]RC=\dfrac{360}{3} \\RC=120[/tex]
Hence the measure of are RC is 120 degrees.
Learn more about arc of circle here;
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