Answer :

calculista

we know that

The measure of the interior angle is the half-sum of the arcs comprising it and its opposite.

so

Find the measure of the angle LAM

m∠LAM is equal to

[tex]\frac{1}{2}*[arc\ KJ+arc\ LM]= \frac{1}{2}*[170+80]\\\\=125\ degrees[/tex]

Find the measure of the angle MAJ

we know that

m∠LAM+m∠MAJ=[tex]180[/tex]° ------> by supplementary angles

m∠MAJ=[tex](180-125)[/tex]

m∠MAJ=[tex]55[/tex]°

therefore

the answer is

The measure of the angle MAJ is [tex]55\ degrees[/tex]

akposevictor

Applying the angles of intersecting chord theorem, m∠MAJ = 55°.

What is the Angles of Intersecting Chord Theorem?

According to the angles of intersecting chord theorem, when two chords intersect, then half of the sum of the measures of the two intercepted arcs equals the measure of the angle formed.

Given:

  • arc JL = 170°
  • arc LM = 80°

Thus:

m∠MAL = 1/2(170 + 80)

m∠MAL = 125°

Therefore:

m∠MAJ =180 - m∠MAL

m∠MAJ = 180 - 125

m∠MAJ = 55°

Therefore, applying the angles of intersecting chord theorem, m∠MAJ = 55°.

Learn more about the angles of intersecting chord theorem on:

https://brainly.com/question/13950364

Other Questions