Answer:
38. x = 60
40. x = 10
Step-by-step explanation:
38.
The segment labeled 30 connects the midpoints of two sides of a triangle, so it is parallel and half the length of the third side.
x = 2 * 30 = 60
40.
Look at the big outer triangle.
Its left side has length x. It is made up of two segments that are congruent.
The right side of the big triangle is made up of two segments that are congruent and are also congruent to the segments of the left side. That makes the left and right sides of the big triangle congruent. This is an isosceles triangle, so its base angles are congruent. The left base angle measures 60, so the right base angle also measures 60. That means the top angle also measures 60. This triangle is isosceles and equilateral.
Since the segment measuring 5 has endpoints that are midpoints of two sides of a triangle, it is parallel to the third side and half its length.
The bottom side of the triangle measures 2 * 5 = 10. Since the triangle is equilateral, then x = 10.
