Given: circle k (O) , m PL =80°, m PY =150° Find: m∠YPL

Question

asked Jun 26, 2020 135k views

2 Answers

Jklp · Answer 1 · 2020-07-03T11:17:45+0000

Answer:

$m\angle YPL=65^(\circ)$

Explanation:

We have been given an image of a circle and we are asked to find the measure of angle YPL.

Since the degree measure of circumference of a circle is 360 degrees, so we can set an equation to find the measure of arc LY as:

$m\widehat{LY}+m\widehat{PL}+m\widehat{PY}=360^(\circ)$

Upon substituting our given values in above equation we will get,

$m\widehat{LY}+80^(\circ)+150^(\circ)=360^(\circ)$

$m\widehat{LY}+230^(\circ)-230^(\circ)=360^(\circ)-230^(\circ)$

$m\widehat{LY}=130^(\circ)$

We can see that angle YPL is inscribed angle of arc LY, so the measure of angle YPL will be half the measure of arc LY.

$m\angle YPL=(1)/(2)m\widehat{LY}$

$m\angle YPL=(1)/(2)*130^(\circ)$

$m\angle YPL=65^(\circ)$

Therefore, the measure of angle YPL is 65 degrees.