Question

I NEED HELPPPP YALL on this :)

Answer 1

a. 35°

b. 6 units

Explanation:

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

`m\angle P = \frac{1} {2} * \bigg(m\widehat{QS} - m\widehat{QR}\bigg) \\\\</p><p>m\angle P = \frac{1} {2} * \bigg(150\degree - 80\degree\bigg) \\\\</p><p>m\angle P = \frac{1} {2} * 70\degree \\\\</p><p>\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:

`</p><p>PQ^2 = PR* PS\\\\</p><p>PQ^2 = 4* 9\\\\</p><p>PQ^2 = 36\\\\</p><p>PQ =\pm \sqrt {36} \\\\</p><p>PQ=\pm 6\\`

Since, PQ can not be a negative number.

So, PQ = 6 units.