Question

[Will mark as brainliest] Can someone help me understand this and help me get the answer?

Answer 1

The intersecting tangents theorem says that the measure of angle PQR is half the difference of the measures of the arcs that the tangents intercept. This means

$m\angle PQR=\dfrac{m\widehat{PR}_{\rm maj}-m\widehat{PR}_{\rm min}}2$

where $\widehat{PR}_{\rm maj}$ refers to the major arc PR, and $\widehat{PR}_{\rm min}$ refers to the minor arc PR (the one you know has measure $(100x)^\circ$).

The major and minor arcs PR form the circle, so their measures add up to 360º:

$m\widehat{PR}_{\rm maj}=360^\circ-(100x)^\circ$

Then by the aforementioned theorem, we have

$(81x-1)^\circ=\dfrac{\left(360^\circ-(100x)^\circ\right)-(100x)^\circ}2$

$81x-1=\dfrac{360-200x}2$

$81x-1=180-100x$

$181x=181$

$\implies x=1$

Then the minor arc PR has measure 100º, making the answer A.