Answer:
measure of arc EI = 140°
Step-by-step explanation:
Given that : arc EY = arc YI , m∠EXY=80°, m∠K=25°
To find : measure of arc EI
Solution :
The arc measure subtended by two chords is half the angle formed by the two chords outside the circle
⇒ arc EI - arc LJ = 2 × m∠K
⇒ arc EI - arc LJ = 2 × 25°
⇒ arc EI - arc LJ = 50° ...........(1)
Similarly, The sum of both the arc measures is twice the angle formed by them inside the circle.
⇒ 0.5 × arc EI + arc LJ = 2 × m∠EXY
⇒ 0.5 × arc EI + arc LJ = 2 × 80°
⇒ 0.5 × arc EI + arc LJ = 160° .......(2)
Adding equations (1) and (2)
⇒ 1.5 × arc EI = 210°
⇒ measure of arc EI = 140°
