X= -2 or X= 3 either one works.
Answer:
Option A.

Step-by-step explanation:
see the attached figure with letters to better understand the problem
In this problem we have a triangle with a circle inscribed in it
so

step 1
Find the length side B.C

substitute the given values

step 2
Find the length side C.D
Remember that

therefore

step 3
Find the length side E.D
we know that

substitute the given values

step 4
Find the length side E.F
Remember that

therefore

step 5
Find the length side A.F
Remember that

therefore

step 6
Find the perimeter


Answer:
15°.
Step-by-step explanation:
1. Angles ADC and CDB are supplementary, thus
m∠ADC+m∠CDB=180°.
Since m∠ADC=115°, you have that m∠CDB=180°-115°=65°.
2. Triangle BCD is isosceles triangle, because it has two congruent sides CB and CD. The base of this triangle is segment BD. Angles that are adjacent to the base of isosceles triangle are congruent, then
m∠CDB=m∠CBD=65°.
The sum of the measures of interior angles of triangle is 180°, therefore,
m∠CDB+m∠CBD+m∠BCD=180° and
m∠BCD=180°-65°-65°=50°.
3. Triangle ABC is isosceles, with base BC. Then
m∠ABC=m∠ACB.
From the previous you have that m∠ABC=65° (angle ABC is exactly angle CBD). So
m∠ACB=65°.
4. Angles BCD and DCA together form angle ACB. This gives you
m∠ACB=m∠ACD+m∠BCD,
m∠ACD=65°-50°=15°.
Have a good Day!