Question

Solve these two questions for 50 pts.

Answer 1

RS = 26

x = 6

Explanation:

Answer 2

• RS = 26
• x = 6

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