Question

Given: mMEJ=30°, mMFJ= 50° Find: mKL, mMJ

Answer 1

Applying the angles of intersecting secants theorem, the measures of the arcs are:

m(KL) = 20°; m(MJ) = 80°.

What is the Angles Intersecting Secants Theorem?

When two secants intersect and form an angle outside the circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs.

Given the following:

• m∠MEJ = 30°
• m∠MFJ = 50°

m∠MEJ = 1/2(MJ - KL)

30 = 1/2(MJ - KL)

60 = MJ - KL

KL = MJ - 60

m∠MFJ = 1/2(MJ + KL)

50 = 1/2(MJ + MJ - 60)

100 = 2MJ - 60

2MJ = 100 + 60

2MJ = 160

MJ = 160/2

MJ = 80°

KL = MJ - 60 = 80 - 60

KL = 20°

Thus, applying the angles of intersecting secants theorem, the measures of the arcs are:

m(KL) = 20°; m(MJ) = 80°.

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