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

Given: m arc IV =114°, m∠VSK=38° Find: m PK-example-1

1 Answer

6 votes

Answer:

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\°

User Lemuel
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