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astra-53 [7]
3 years ago
8

Central Angles and Arc Measures Practice What is X?

Mathematics
1 answer:
myrzilka [38]3 years ago
7 0

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}

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