Triangle a b c is cut by line segment m n. line segment m n goes from side a b to side b c. the length of m n is 9 feet. the lengths of b m and m a are 4 feet. the lengths of b n and n c are 3 feet. what is the length of line segment a c? 3 ft 4 ft 9 ft 18 ft

The length of AC is 18 feet ⇒ 4th answer

Step-by-step explanation:

* Lets revise an important theorem for a triangle

- If a line segment joining the mid-points of two sides of a triangle,

  then this line segment is parallel to the third side of the triangle and

  equal half its length

* Lets use this theorem to solve the problem

- In Δ ABC

∵ Line MN intersects the sides AB at M

∵ MA = MB

∴ M is the mid point of the side AB

∵ Line MN intersects the sides BC at N

∵ NC = NB

∴ N is the mid point of the side BC

- By using the theorem above

  In Δ ABC

∵ M is the mid-point of AB

∵ N is the mid-point of BC

∴ MN // AC

∴ MN = AC

∵ The length of MN = 9 feet

∵ MN = AC

∴ 9 = AC

- Multiply both sides by 2

∴ AC = 18 feet

* The length of AC is 18 feet

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.