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given: m arc ey = m arc yi

m∠exy=80°, m∠k=25°

find: m arc ei

140 degrees

Step-by-step explanation:

50 = EI - LJ

160 = 1/2 EI + LJ

210 = 1.5 EI

EI = 140

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°

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step-by-step explanation:

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