Given:
m(ar QT) = 220
m∠P = 54
To find:
The measure of arc RS.
Solution:
PQ and PT are secants intersect outside a circle.
If two secants intersects outside a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
[tex]$\Rightarrow \angle P = \frac{1}{2} (m \ ar (QT) - m \ ar (RS ))[/tex]
[tex]$\Rightarrow 54 = \frac{1}{2} (220- m \ ar (RS ))[/tex]
Multiply by 2 on both sides.
[tex]$\Rightarrow 2 \times 54 = 2 \times \frac{1}{2} (220- m \ ar (RS ))[/tex]
[tex]$\Rightarrow 108= 220- m \ ar (RS )[/tex]
Subtract 220 from both sides.
[tex]$\Rightarrow 108-220= 220- m \ ar (RS )-220[/tex]
[tex]$\Rightarrow -112= -m \ ar (RS )[/tex]
Multiply by (-1) on both sides.
[tex]$\Rightarrow (-112)\times(-1)= -m \ ar (RS )\times(-1)[/tex]
[tex]$\Rightarrow 112= m \ ar (RS )[/tex]
The measure of arc RS is 112.
