Answer:
1. BC = 18
2. m<ABC = 80°
3. x = 5
Step-by-step explanation:
1. If DE = 9, therefore:
[tex] BC = 2 \times 9 = 18 [/tex] (based on the midsegment theorem, DE is half the length of the third side, BC)
2. m<ADE = 80°, then,
m<ABC = 80°
This is because m<ADC and m<ABC are corresponding angles. Corresponding angles are congruent.
3. DE = 2x + 7 , and BC = 7x - 1, find BC
Thus:
[tex] BC = 2 \times DE [/tex] (midsegment theorem)
[tex] 7x - 1 = 2 \times (2x + 7) [/tex] (substitution)
Solve for x
[tex] 7x - 1 = 4x + 14 [/tex]
Collect like terms
[tex] 7x - 4x = 1 + 14 [/tex]
[tex] 3x = 15 [/tex]
Divide both sides by 3
x = 5
