Question

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

Answer 1

Answer:

$ED = 26$

$CF = 13$

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

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

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

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

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

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

Answer 2

Following are the calculated value " $ED=26, CF=13\ , m \widehat{ED}=136^{\circ}\ , m \widehat{HD}=68^{\circ}\ , m \widehat{CE}=88^{\circ}$", and its complete calculation can be defined as follows:

Given value:

$\bold{JG=JF,GD=13,} \\\\ m \widehat{CD}=136^{\circ}$

When

$m \widehat{CD}= m \widehat{ED}\\\\m \widehat{ED} = 136^{\circ}$

$HJ \perp CD \\\\IJ \perp ED$

SO,

$CF = FD \\\\EG=ED$

$m \widehat{HD} = m \widehat{CH} = \frac{1}{2} m \widehat{CD}$

$CF=13\\\\ ED = 13 \times 2 =26 \\\\ m \widehat{HD} = \frac{1}{2}\ m \widehat{CD} = 136^{\circ} \div 2 = 68^{\circ}\\\\m \widehat{CE} = 360^{\circ} -136^{\circ} - 136^{\circ} = 88^{\circ}$

Using the Vertical theorem and Theorem of the length of tangent to calculate the value:

$ED=26\\\\CF=13\\\\m \widehat{ED}=136^{\circ}\\\\m \widehat{HD}=68^{\circ}\\\\m \widehat{CE}=88^{\circ}$

Note:

The given question is incomplete that's why we defined the question in the attached file and then solve it.

Find out more information about the arc of the circle here:

brainly.com/question/1577784