Segments b and c are parallel. What is the value of x?

x = 8

Step-by-step explanation:

From the figure attached,

'b' and 'c' are the parallel lines and line 'a' is a transversal line intersecting parallel lines at the points respectively.

Line 'a' is perpendicular to line 'b'.

Angle between lines 'a' and 'b' is 90°.

Therefore, m(∠X) + 90° = 180° [Linear pair of angles]

m(∠X) = 90°

Since, angle X and angle having measure [5(x + 7) + 15]° are the corresponding angles,

m(∠X) = [5(x + 7) + 15]°

90° = [5(x + 7) + 15]°

5(x + 7) = 90 - 15

5(x + 7) = 75

x + 7 = 15

x = 8

Therefore, x = 8 will be the answer.

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.