Given: lines a and b are parallel and line c is a transversal.

prove: angle2 is supplementary to angle8

horizontal and parallel lines a and b are cut by transversal c. on line a where it intersects line c, 4 angles are created. labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. on line b where it intersects line c, 4 angles are created. labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7.

what is the missing reason in the proof?

statement reason

1. a || b, is a transv 1. given

2. ∠6 ≅ ∠2 2. ?

3. m∠6 = m∠2 3. def. of congruent

4. ∠6 is supp. to ∠8 4. def. of linear pair

5. ∠2 is supp. to ∠8 5. congruent supplements theorem

corresponding angles theorem

alternate interior angles theorem

vertical angles theorem

alternate exterior angles theorem

question is incomplete.

mnkjn

step-by-step explanation:

$75.00

step-by-step explanation:

i = prt

i = 1,5000 * 0.025 * 2

i = 75

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9