Given:
Measure of arcs 50°, 115° and 85°
To find:
The measure of the numbered angle 5.
Solution:
Let the missing arc measure be A.
The arc measure of a full circle is 360°
m(ar A) + 50° + 115° + 85° = 360°
m(ar A) + 250° = 360°
Subtract 250 from both sides.
m(ar A) = 110°
If two chords intersects inside a circle, then the measure of the angle formed is half of the sum of intercepted arcs.
[tex]$\Rightarrow m\angle 5 =\frac{1}{2} (110^\circ+115^\circ)[/tex]
[tex]$\Rightarrow m\angle 5 =\frac{1}{2} (225^\circ)[/tex]
[tex]$\Rightarrow m\angle 5 =112.5^\circ[/tex]
The measure of the numbered angle is 112.5°.
