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

Question

asked Jul 17, 2020 154k views

1 Answer

Glebcom · Answer 1 · 2020-07-21T17:54:56+0000

Answer:

The measure of the
${\angle}VPL$ is
$80^(\circ)$

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

$m{\angle}ISV={(1)/(2)}(x+y)$

Substituting the given values, we get

$135^(\circ)={(1)/(2)(140^(\circ)+y)$

$270^(\circ)=140^(\circ)+y$

$y=130^(\circ)$

Thus, The measure of arc PK is
$130^(\circ)$ .

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

$m{\angle}VPL={(1)/(2)(z+y)$

Substituting the values, we get

$m{\angle}VPL={(1)/(2)}(30+130)=80^(\circ)$

Hence, the measure of the
${\angle}VPL$ is
$80^(\circ)$ .