ANSWER
[tex] \angle \: KGI =50 \degree[/tex]
[tex]\angle \: KJI = 130 \degree[/tex]
EXPLANATION
Angles in the same segment are equal.
This implies that;
[tex] \angle \: KGI = \angle \:H[/tex]
Hence,
[tex] \angle \: KGI =50 \degree[/tex]
Also GJKI is a cyclic quadrilateral.
The opposite angles of a cyclic quadrilateral sums up to 180°.
This means that,
[tex] \angle \: KJI + \angle \: KGI = 180 \degree[/tex]
[tex] \angle \: KJI +50 \degree = 180 \degree[/tex]
[tex]\angle \: KJI = 180 \degree - 50 \degree[/tex]
[tex]\angle \: KJI = 130 \degree[/tex]
