Question

In circle O, what is m∠MAJ? °

Answer 1

See the attached figure.

m ∠KAJ = 170° &  m ∠LAM = 80°

We should know that :

m ∠KAJ + m ∠LAM + m ∠KAL + m ∠MAJ = 360°

∴ m ∠KAL + m ∠MAJ = 360° - (m ∠KAJ + m ∠LAM)

∴ m ∠KAL + m ∠MAJ = 360° - (170°+80°) = 360° - 250° = 110°

But : m ∠KAL = m ∠MAJ ⇒⇒⇒ Opposite angles.

∴ m ∠MAJ + m ∠MAJ = 110°

∴ 2 * m ∠MAJ = 110°

∴ m ∠MAJ = 110° ÷ 2 = 55°

So, the answer is :  m ∠MAJ = 55°