Question

Given: m arc IV =114°, m∠VSK=38° Find: m PK

Answer 1

Answer:

The measure of arc PK is $170\°$

Step-by-step explanation:

step 1

Find the measure of angle ISV

we know that

$m<ISV+m<VSK=180\°$ -----> by supplementary angles

we have

$m<VSK=38\°$

substitute

$m<ISV+38\°=180\°$

$m<ISV=180\°-38\°=142\°$

step 2

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

$142\°=\frac{1}{2}(114\°+y)$

$284\°=(114\°+y)$

$y=284\°-114\°=170\°$