Given: arc iv =140°, arc vk =30°, m∠isv=135, find: m∠vpl

The measure of the is

Step-by-step explanation:

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

Now, Let

x is the measure of arc IV

and y is the measure of arc PK, then

Substituting the given values, we get

Thus, The measure of arc PK is .

Also, we know that  the inscribed angle measures half that of the arc comprising , thus

Let

z is the measure of arc VK

and  y is  the measure of arc PK, then

Substituting the values, we get

Hence, the measure of the is .

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step-by-step explanation:

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