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
<u>(x - 45) + (x - 12) = x</u>
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
<u>x = 57</u><u> Subtract x from both sides</u>
Finding m∠D:
x - 45 = ?
<u>57 - 45 = </u><u>12º </u>
Finding m∠C:
x - 12 = ?
<u>57 - 12 = </u><u>45º </u>
<em>** </em><em>(Checking x: 12 + 45 = 57) </em><em>**</em>
<em>Finding </em>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,
❤<em>A.W.E.</em><u><em>S.W.A.N.</em></u>❤
To construct a perpendicular bisector, we have to draw two arcs using each of the endpoints as centers
<h3>What is a perpendicular bisector?</h3>
A perpendicular bisector is said to be a line that intersects the segment of another line perpendicularly and also divides it into two equal parts.
The properties of a perpendicular bisector include:
- It divides a line segment into two equal parts
- It makes right angles with the line segment.
- Points in the perpendicular bisector are equal from the line of the segment.
Hence, all the mentioned properties are correct except that to construct it, we have to draw two arcs using each of the endpoints as centers.
Learn more about perpendicular bisector here:
brainly.com/question/21752287
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Answer:
x=6
Step-by-step explanation:
Hope it was right