Question

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

Answer 1

Answer:

YL=130 (PWP)

m<YPL=65 (Inscribed < th)

Step-by-step explanation:

Answer 2

Answer:

$m\angle YPL=65^{\circ}$

Step-by-step 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.

$m\angle YPL=\frac{1}{2}m\widehat{LY}$

$m\angle YPL=\frac{1}{2}\times130^{\circ}$

$m\angle YPL=65^{\circ}$

Therefore, the measure of angle YPL is 65 degrees.