Question

In circle O, what is m∠MAJ?

Answer 1

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

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

Find the measure of the angle MAJ

we know that

m∠LAM+m∠MAJ=$180$° ------> by supplementary angles

m∠MAJ=$(180-125)$

m∠MAJ=$55$°

therefore

the answer is

The measure of the angle MAJ is $55\ degrees$

Answer 2

55 degrees because the area of a circle adds up to 360. when you add 170 and 80 you get 250. subtract 250 from 360 and you'd get 110. since mLAK and mMAJ are similar, you divide 110 by 2 and get 55