Answer:
Step-by-step explanation:
Question 1
V and W are midpoints of RU and ST ⇒ VW is a midsegment
VW = 1/2(RS + UT) ⇒ RS = 2*VW - UT
Substitute values:
- 2x + 15 = 2(2x + 5) - (6x - 37)
- 2x + 15 = 4x + 10 - 6x + 37
- 2x + 15 = -2x + 47
- 2x + 2x = 37 - 15
- 4x = 22
- x = 5.5
RS = 2x + 15 = 2(5.5) + 15 = 11 + 15 = 26
Question 2
- Trapezoid given with congruent sides, JM = KL
- Angle J and K are congruent, both are (7x + 2)
- Angles M and L are congruent, both are (2x - 14)
J and M are supplementary, so sum to 180°
- 7x + 2 + 25x - 14 = 180
- 32x = 192
- x = 192/32
- x = 6
