What is m angle H + m angle J?

180°

Step-by-step explanation:

The measure of an inscribed angle (inscribed inside a circle) is half the measure of its inscribed arc.

m∡H = (1/2)(m arc GJI)

m∡J = (1/2)(m arc GHI)

m∡H + m∡J = (1/2)(m arc GJI + m arc GHI)

But those two arcs added together on the right side are the whole circle, so they add to 360°.

m∡H + m∡J = (1/2)360°

m∡H + m∡J = 180°

; )

step-by-step explanation: ; )