Find the missing terms of the following geometric sequence. Assume all terms are positive. (Hint: The geometric mean of the first and fifth terms is the third term.) 0.5,__,__,__,312.5,...

see explanation

Step-by-step explanation:

(1)

Δ RTW and Δ RSW are right triangles

The sum of the 3 angles in a triangle = 180°

∠ 1 = 180° - 90° - 60° = 180° - 150° = 30°

∠ 2 = 180° - 90° - 30° = 180° - 120° = 60°

(2)

∠ 1 = 180° - 58° - 66° = 180° - 124° = 56°

∠ 1 and ∠ 2 are vertically opposite angles and are congruent , so

∠ 2 = 56°

∠ 3 = 180° - 56° - 50° = 180° - 106° = 74°

(3)

∠ 1 = 180° - 35° - 36° = 180° - 71° = 109°

∠ RVU and ∠ 1 are adjacent angles on a straight line and sum to 180° , then

∠ RVU = 180° - ∠ 1 = 180° - 109° = 71°

∠ 2 = 180° - 71° - 80° = 180° - 151° = 29°

Similarly ∠ 1 and ∠ 3 are adjacent angles and sum to 180° , then

∠ 3 = 180° - ∠ 1 = 180° - 109° = 71°

(4)

∠ 1 and ∠ 2 are congruent angles , then

∠ 1 = ∠ 2 = = = 67°