Question

Central Angles and Arc Measures Practice

What is X?

Answer 1

Answer:
`5^(\circ)`

Explanation:

Given

`\angle DIE=(18x-2)^(\circ)\\\angle DIH=15^(\circ)\\\angle FIG=103^(\circ)`

from the figure

`\angle HIE=\angle GIF\quad [\text{vertically opposite angles}]\\\angle HID+\angle DIE=\angle GIF\\15^(\circ)+(18x)^(\circ)-2^(\circ)=103^(\circ)\\(18x)^(\circ)=103^(\circ)-13^(\circ)\\\\x=(90^(\circ))/(18)\\\\x=5^(\circ)`