Question

I need help is for geometry

Answer 1

Answers:
mAE = 78°
mABD = 206°
mDA = 154°
mBCE = 255°
mECA = 282°
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Explanation:
The total arc measure of a circle is 360.

This circle shows that mDE has the same arc as mDC. mDC's arc will equal 76.

To find mAE, add all the known arc values, set mAE to x, and set the equation equal to 360.

$27 + 103 + 76 + 76 + x = 360$

Combine all like terms.

$27 + 103 = 130$
$76 + 76 = 152$
$130 + 152 = 282$

$282 + x = 360$

Subtract 360 from both sides to get x by itself.

$x = 78$

The arc measure of mAE is 78.


Now we can find all of the arc values.

mAE = 78°

mABD = measure of mAB + mBD
$27 + (103 + 76) = 27 + 179 = 206$

mABD = 206°

mDA = mDE + mEA

$76 + 78 = 154$

mDA = 154°

mBCE = mBC + mCD + mDE

$103 + 76 + 76 = 179 + 76 = 255$

mBCE = 255°

mECA = mED + mDC + mCB + mBA

$76 + 76 + 103 + 27 = 152 + 130 = 282$

mECA = 282°