Question

Given: The measure of arc EY = The measure of arc YI, m∠EXY = 80°, and m∠K = 25°.

Answer 1

Answer:

Step-by-step explanation:

Let . By the inscribed angle theorem, we have

Then

Also by the inscribed angle theorem, we have

so that

Angles EXY and LXJ form a vertical pair so they are congruent and both have measure .

The sum of the interior angles to any quadrilateral is , so for quadrilateral KLXJ we get

So,

Read more on Brainly.com - brainly.com/question/12616099#readmore

Answer 2

Let $x=m\widehat{EY}=m\widehat{YI}$. By the inscribed angle theorem, we have

$m\angle EJI=\dfrac12m\angle EOI=\dfrac12m\widehat{EI}=\dfrac{m\widehat{EY}+m\widehat{YI}}2=x^\circ$

Then

$m\angle KJE=(180-x)^\circ$

Also by the inscribed angle theorem, we have

$m\angle ELY=\dfrac12m\angle EOY=\dfrac12m\widehat{EY}=\left(\dfrac x2\right)^\circ$

so that

$m\angle KLX=\left(180-\dfrac x2\right)^\circ$

Angles EXY and LXJ form a vertical pair so they are congruent and both have measure $80^\circ$.

The sum of the interior angles to any quadrilateral is $360^\circ$, so for quadrilateral KLXJ we get

$25^\circ+\left(180-\dfrac x2\right)^\circ+(180-x)^\circ+80^\circ=360^\circ\implies x^\circ=70^\circ$

So,

$m\widehat{EI}=2x^\circ=\boxed{140^\circ}$