Question

what is ( mangle hij )?
write your answer as an integer or decimal.
( mangle hij = square^circ )

Explanation:

Step1: Find $\angle HGJ$

The sum of angles around point $G$ is $360^\circ$.
$$\angle HGJ = 360^\circ - 136^\circ - 118^\circ = 106^\circ$$

Step2: Find arc $HJ$

Central angle equals its arc measure.
$$m\overset{\frown}{HJ} = \angle HGJ = 106^\circ$$

Step3: Find $\angle HIJ$

Inscribed angle is half its intercepted arc.
$$m\angle HIJ = \frac{1}{2} \times m\overset{\frown}{HJ}$$
$$m\angle HIJ = \frac{1}{2} \times 106^\circ = 53^\circ$$

Answer:

$53$