Question

Given: circle k(O), m∠P=95°, m∠J=110°, m∠LK=125° Find: m∠PJ

Answer 1

Answer:

The measure of the arc PJ is $75\°$

Step-by-step explanation:

step 1

Find the measure of angle L

we know that

In a inscribed quadrilateral opposite angles are supplementary

so

$m$

we have

$m$

substitute

$m$

$m$

step 2

Find the measure of arc KJ

we know that

The inscribed angle measures half that of the arc comprising

so

$m$

substitute the values

$95\°=\frac{1}{2}(125\°+arc\ KJ)$

$190\°=(125\°+arc\ KJ)$

$arc\ KJ=190\°-125\°=65\°$

step 3

Find the measure of arc PJ

we know that

The inscribed angle measures half that of the arc comprising

so

$m$

substitute the values

$70\°=\frac{1}{2}(65\°+arc\ PJ)$

$140\°=(65\°+arc\ PJ)$

$arc\ PJ=140\°-65\°=75\°$