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2 years ago

If c is the incenter of AMD, AMC=3x+6 AND dmc = 8X-49, FIND EACH MEASURE

Mathematics

2 answers:

NARA [144]2 years ago

5 0

3x+6=8x-49,
-6. -6
__________
3x=8x-55
-8x. -8x
________
-5x=-55
x=11,
3(11)+6=39
8(11)-49=39

777dan777 [17]2 years ago

3 0

Answer:

$m\angle AMC = 39\°$ and $m\angle DMC = 39\°$ .

Step-by-step explanation:

As you can observe in the image attached, angles AMC and DMC are congruent, because if point C is the incenter of AMD, that means each line the forms such point is a bisector.

Remember that a bisector is a line that equally divides an angle.

So,

$\angle AMC = \angle DMC\\3x+6=8x-49$

Solving for $x$ , we have

$6+49=8x-3x\\5x=55\\x=11$

Then, we substitute this value in each expression to find the angles.

$\angle AMC = 3x+6 = 3(11)+6=33+6=39$

$\angle DMC = 8(11)-49=88-49=39$

Therefore, the measures of those angles are $m\angle AMC = 39\°$ and $m\angle DMC = 39\°$ .

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Answer:

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