To find the measure of the intercepted arc, we need to use the formula:

• Intercepted arc = (Central angle / 360) x Circumference of the circle

Note that the circumference of the circle is given by:

• Circumference = 2 x pi x radius

• Where pi is approximately equal to 3.14.

Using this formula, we can solve for the measure of the intercepted arc for each central angle:

1. 45°

Intercepted arc = (45 / 360) x 2 x pi x radius

Intercepted arc = (1/8) x 2 x pi x radius

Intercepted arc = 0.25 x pi x radius

2. 90°

Intercepted arc = (90 / 360) x 2 x pi x radius

Intercepted arc = (1/4) x 2 x pi x radius

Intercepted arc = 0.5 x pi x radius

3. 145°

Intercepted arc = (145 / 360) x 2 x pi x radius

Intercepted arc = (29/72) x 2 x pi x radius

Intercepted arc = 0.402 x pi x radius

4. 160°

Intercepted arc = (160 / 360) x 2 x pi x radius

Intercepted arc = (4/9) x 2 x pi x radius

Intercepted arc = 0.8889 x pi x radius

5. 177°

Intercepted arc = (177 / 360) x 2 x pi x radius

Intercepted arc = (59/120) x 2 x pi x radius

Intercepted arc = 0.4917 x pi x radius

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