Question

Central Angles and Arc Measures Practice What is X?

Answer 1

Answer: $5^{\circ}$

Step-by-step explanation:

Given

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

from the figure

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