Question

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

Answer 1

The measure of arc PK is
`170\°`

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=(1)/(2)(x+y)`

substitute the values and solve for y

`142\°=(1)/(2)(114\°+y)`

`284\°=(114\°+y)`

`y=284\°-114\°=170\°`