Answer:
Correct choices are A and C
Step-by-step explanation:
Inscribed angles property: The inscribed angles subtended by the same arc are equal.
1. Angles EFH and EGH are both inscribed angles subtended by the arc EH. Therefore, these angles are congruent (option A is true).
2. Angles GHF and GEF are both inscribed angles subtended by the arc GF. Therefore, these angles are congruent (option C is true).
3. Angles EGH and FHG are interior angles of the triangle KGH and can be congruent (if triangle is isosceles) or can be not congruent (in general). Thus, option B is false.
4. Angles EFH and FHG in general are not congruent. They can be congruent only when arcs EH and FG have the same measure. In general, option D is false.
We know Angle HMK is half the sum of Arc JI and Arc HLK. So, we can set up an equation.
8x - 1 = 1/2 (3x + 2 + 15x - 36)
8x - 1 = 1/2 (18x - 34)
16x - 2 = 18x - 34
32 = 2x
16 = x
Then, we can substitute x into Arc HLK
HLK = 15x - 36
HLK = 240 - 36
Arc HLK = 204°
Answer:
the answer would be 47/40
The answer to your question is 41
