The clock face on London's Big Ben measures 23 feet across. How far does the tip of the minute hand travel between 6:50 and 7:30?

48.15 feets

Explanation:

Diameter = 23 feet (measure of clock face)

Hence, The Circumference, C of London's big ben = πd

π = 3.14

Circumference = 3.14 * 23 = 72.22 feets

Between 6:50 to 7:30 = 40 minutes

40 minutes / 60 minutes = 2 /3 of the Circumference

2/3 * Circumference

2/3 * 72.22 feets

= 48.146 feets

Distance traveled = 48.15 feets

if triangle abc is congruent to triangle def, their interior angles are congruent, because congruent parts of congruent triangles are congruent (cpctc).

that means ∠d is congruent to ∠a; ∠d is equal to 8x - 2.

interior angles of all triangles add to equal 180 degrees, so you can set the sum of these interior angle values equal to 180 and solve for x.

180 = (8x - 2) + 22 + 72

180 = 8x - 2 + 22 + 72

180 = 8x + 92

88 = 8x

11 = x

x = 11