German: If JG = JF, =13, and mCD =136, find each measure

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02.05.2023

If JG = JF, =13, and mCD =136, find each measure

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Mathematics

If JG=JF,GD=13, and mCD=136, find each measure.

Step-by-step answer

P Answered by Master

ED = 26

CF = 13

$m \overset{\huge\frown}{ED} = 136$

$m \overset{\huge\frown}{HD} = 68$

$m \overset{\huge\frown}{CE} =88$

Step-by-step explanation:

Given

JG = JF

GD = 13

$m \overset{\huge\frown}{CD} = 136$

See attachment for circle

Solving (a): Length ED

Line JD divides ED into two equal parts, EG and DG.

So:

ED = EG + GD

ED = GD + GD

ED = 13 + 13

ED = 26

Solving (b): Length CF

CF is a reflection of EG.

So:

CF = EG

EG = GD = 13

So:

CF = 13

Solving (c): $m \overset{\huge\frown}{ED}$

Since ED = CD;

Then:

$m \overset{\huge\frown}{ED} = m \overset{\huge\frown}{CD}$

So:

$m \overset{\huge\frown}{ED} = 136$

Solving (d): $m \overset{\huge\frown}{HD}$

Line HF divides CD to 2 equal parts

So:

$m \overset{\huge\frown}{HD} = \frac{1}{2} * m \overset{\huge\frown}{CD}$

$m \overset{\huge\frown}{HD} = \frac{1}{2} * 136$

$m \overset{\huge\frown}{HD} = 68$

Solving (e): $m \overset{\huge\frown}{CE}$

$m \overset{\huge\frown}{CE}$ is a minor arc while $m \overset{\huge\frown}{ED} = 136$ + $m \overset{\huge\frown}{CD} = 136$ are the major arcs.

So:

$m \overset{\huge\frown}{CE} + m \overset{\huge\frown}{ED} + m \overset{\huge\frown}{CD}= 360$

$m \overset{\huge\frown}{CE} + 136+136= 360$

Collect like terms

$m \overset{\huge\frown}{CE} =- 136-136+ 360$

$m \overset{\huge\frown}{CE} =88$

If JG=JF,GD=13, and mCD=136, find each measure.

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Step-by-step answer

P Answered by PhD

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Step-by-step answer

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Step-by-step answer

P Answered by PhD

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Step-by-step answer

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