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Hunter-Best [27]
3 years ago
10

I'm given 1/4 of a circle, how to find the rest of it

Mathematics
1 answer:
DiKsa [7]3 years ago
3 0
Let's x be the rest of it.
x=1-1/4
x=4/4-1/4
x=3/4
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Substituting the given expression for each segment in the first equation, we get:

3x+6=2(2x-2).

Solving the above equation for x, we get:

\begin{gathered} 3x+6=4x-4, \\ 3x+6+4=4x, \\ 3x+10=4x, \\ 4x-3x=10, \\ x=10. \end{gathered}

Substituting x=10 in the equation for segment EI, we get:

EI=2*10-2=20-2=18.

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Now, to determine the measure of angle IEH, we notice that:

\Delta HFG\cong\Delta GEH,

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\measuredangle GHF\cong\measuredangle HGE.

Using the facts that the triangles are right triangles and that the interior angles of a triangle add up to 180° we get:

m\measuredangle IEH=90^{\circ}-35^{\circ}=55^{\circ}.

<h2>Answer: </h2>\begin{gathered} m\operatorname{\measuredangle}IEH=55^{\operatorname{\circ}}, \\ GI=18. \\  \end{gathered}

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