Question

Please answer fast!!! Will give brainliest!!!given: m∠EYL= 1/3 m arc EHL Find: m∠EYL.

Answer 1

Answer:

The measure of angle EYL is $45\°$

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs which comprises

Let

x-----> the measure of arc EVL

y----> the measure of arc EHL

$m$

$m$

so

$\frac{1}{3}y=\frac{1}{2}(x-y)$

Multiply by 6 both sides

$2y=3x-3y$

$3x=5y$

$x=\frac{5}{3}y$ -----> equation A

$x+y=360\°$ -----> equation B  ( is a complete circle)

substitute equation A in equation B

$\frac{5}{3}y+y=360\°$

$\frac{8}{3}y=360\°$

$y=(360\°)*(3)/8=135\°$

Find the value of x

$x=\frac{5}{3}(135\°)=225\°$

Find the measure of angle EYL

$m$

substitute the values

$m$