Answer:
Therefore the measure of this angle is [tex]=(\frac{43}{90} )^\circ[/tex]
Step-by-step explanation:
Given, a circle is centered at the vertex of an angle and the angle's rays subtend an arc that is 86 cm long.
0.5 cm arc make an angle [tex]\frac{1}{360}[/tex]
1 cm arc make an angle [tex]\frac{1}{360\times 0.5}[/tex]
86 cm arc make an angle [tex]\frac{86}{360\times 0.5}[/tex]
[tex]=(\frac{43}{90} )^\circ[/tex]
Therefore the measure of this angle is [tex]=(\frac{43}{90} )^\circ[/tex]
A circle is centered at the vertex of an angle, and the angle's rays subtend an arc that is 86 cm long. The measure of this angle in degrees is 172°
From the given information:
The total circumference of the circle now will be:
= 360 × 0.5 cm
= 180 cm
However, if a total circumference of 180 cm is equivalent to an angle of 360°;
Then, an angle that subtends with 86 cm long will be:
[tex]\mathbf{=\dfrac{86 \ cm }{180 \ cm } \times 360^0 }[/tex]
= 172°
Therefore, the measure of this angle is 172°
Learn more about the circumference of a circle here:
https://brainly.com/question/10079265?referrer=searchResults
