Answer:
2. C, D
3. 30
Explanation:
2. You want the true statements about the diagram that tells you ∠JMK = (6x+2)°, ∠KML = (4x+3)°, and ∠JML = 85°.
3. You want the measure of BC such that (AB=2x+2) +(BC=3x+6) = (AC=48).
2. Angle relations
The whole is the sum of the parts:
∠JMK +∠KML = ∠JML
(6x+2)° +(4x+3)° = 85° . . . substitute given values
10x +5 = 85 . . . . . . . . . . divide by ° and simplify
10x = 80 . . . . . . . . . . subtract 5
x = 8 . . . . . . . . . . . . divide by 10
∠JMK = (6×8 +2)° = 50°
∠KML = (4×8 +3) = 35°
The true statements are C and D.
3. Segment relations
The whole is the sum of the parts:
AB +BC = AC
(2x +2) +(3x +6) = 48 . . . . . . . substitute given values
5x +8 = 48 . . . . . . . . . . . . . collect terms
5x = 40 . . . . . . . . . . . . . . subtract 8
x = 8 . . . . . . . . . . . . . . divide by 5
BC = 3×8 +6 = 30
The length of segment BC is 30 units.