Question

I NEED HELPPPP YALL on this :)

Answer 1

Answer:

a. 35°

b. 6 units

Step-by-step explanation:

a. By the property of intersecting tangent and secant outside of a circle, we have:

$m\angle P = \frac{1} {2} \times \bigg(m\widehat{QS} - m\widehat{QR}\bigg) \\\\

m\angle P = \frac{1} {2} \times \bigg(150\degree - 80\degree\bigg) \\\\

m\angle P = \frac{1} {2} \times 70\degree \\\\

\huge\purple {\boxed{m\angle P =35\degree}}$

b.

$PS = PR + RS = 4 + 5 = 9\: units$

By the property of intersecting tangent and secant outside of a circle, we have:

$

PQ^2 = PR\times PS\\\\

PQ^2 = 4\times 9\\\\

PQ^2 = 36\\\\

PQ =\pm \sqrt {36} \\\\

PQ=\pm 6$

Since, PQ can not be a negative number.

So, PQ = 6 units.