Question

Find m∠DEC (the picture is not drawn to scale).

Answer 1

Answer:

M∠DEC equals 123º.

Step-by-step explanation:

The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.

180 - {(x - 45)+(x - 12)} = m∠DEC

m∠DEC + x = 180

(x - 45) + (x - 12) = x

Solving for x:

(x - 45) + (x - 12) = x

x - 45 + x - 12 = x                             Remove parenthesis

2x - 57 = x                                       Combine like terms

2x = x + 57                                      Add 57 to both sides

x = 57                                             Subtract x from both sides

Finding m∠D:

x - 45 = ?

57 - 45 = 12º                                          

Finding m∠C:

x - 12 = ?

57 - 12 = 45º                                          

** (Checking x: 12 + 45 = 57) **

Finding m∠DEC:

AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:

180 - 57 = 123º

Hope this helps,

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