Question

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

Answer 1

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

Answer 2

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

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\°`.