A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
An arc is one of the portions of a circle. It is basically a part of the circumference of a circle.
The measure of the ∠d is 65 degrees.
The measure of the ∠c is 89 degrees.
The measure of the arc a is 131 degrees.
The measure of arc b is 47 degrees.
We have to determine
The value of each variable. For the circle, the dot represents the center.
What is the angle?
A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
What is an arc?
An arc is one of the portions of a circle. It is basically a part of the circumference of a circle.
1. The measure of ∠d is;
∠d+ 115°= 180°
∠d= 180°-115°= 65°
The measure of the ∠d is 65 degrees.
2. The measure of ∠c is,
∠c+ 91°= 180°
∠c =180°-91° =89°
The measure of the ∠c is 89 degrees.
3. The measure of arc a is,
The inscribed angle measures half that of the arc comprising;
[tex]\rm 115=\dfrac{1}{2}[99+arc \ a]\\\\230=[99+arc a]\\\\arc \ a = 230-99\\\\arc \ a= 131[/tex]
The measure of the arc a is 131 degrees.
4. The measure of arc b is,
The inscribed angle measures half that of the arc comprising;
[tex]\rm 89=\dfrac{1}{2}[131+arc \ b]\\\\178=[131+arc \ b]\\\\arc \ b = 178-131\\\\arc \ b = 47[/tex]
The measure of arc b is 47 degrees.
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