Question

Given: m arc IV =140°, m arc VK =30°, m∠ISV=135° Find: m∠VPL

Answer 1

Answer:

$m<VPL=80\°$

Step-by-step explanation:

step 1

Find the measure of arc PK

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

Let

x------> the measure of arc IV

y ------> the measure of arc PK

$m<ISV=\frac{1}{2}(x+y)$

substitute the values and solve for y

$135\°=\frac{1}{2}(140\°+y)$

$270\°=(140\°+y)$

$y=270\°-140\°=130\°$

The measure of arc PK is $130\°$

step 2

Find the measure of angle VPL

we know that

The inscribed angle measures half that of the arc comprising

Let

z------> the measure of arc VK

y ------> the measure of arc PK

$m<VPL=\frac{1}{2}(z+y)$

substitute the values

$m<VPL=\frac{1}{2}(30\°+130\°)=80\°$