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

1. BC = 18

2. m<ABC = 80°

3. x = 5

Step-by-step explanation:

1. If DE = 9, therefore:

(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:

(midsegment theorem)

(substitution)

Solve for x

Collect like terms

Divide both sides by 3

x = 5

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b