Question

I’ve never been so confused, this is due in a few minutes, pls help if you can!

Answer 1

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.

$\Rightarrow \angle P = \frac{1}{2} (m \ ar (QT) - m \ ar (RS ))$

$\Rightarrow 54 = \frac{1}{2} (220- m \ ar (RS ))$

Multiply by 2 on both sides.

$\Rightarrow 2 \times 54 = 2 \times \frac{1}{2} (220- m \ ar (RS ))$

$\Rightarrow 108= 220- m \ ar (RS )$

Subtract 220 from both sides.

$\Rightarrow 108-220= 220- m \ ar (RS )-220$

$\Rightarrow -112= -m \ ar (RS )$

Multiply by (-1) on both sides.

$\Rightarrow (-112)\times(-1)= -m \ ar (RS )\times(-1)$

$\Rightarrow 112= m \ ar (RS )$

The measure of arc RS is 112.