Question

1) IF DE = 9, find BC

2) if m<ADE = 80, then find m< ABC
3) If DE = 2x + 7 , and BC = 7x - 1, find BC​

Answer 1

1. BC = 18

2. m<ABC = 80°

3. x = 5

Explanation:

1. If DE = 9, therefore:

`BC = 2 * 9 = 18` (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:

`BC = 2 * DE` (midsegment theorem)

`7x - 1 = 2 * (2x + 7)` (substitution)

Solve for x

`7x - 1 = 4x + 14`

Collect like terms

`7x - 4x = 1 + 14`

`3x = 15`

Divide both sides by 3

x = 5