A circle is divided into three arcs in the ratio of 3:4:5. Find the measure of an inscribed angle that intercepts the largest arc.

Question

Macie Stephenson

Mathematics

3 December, 16:52

A circle is divided into three arcs in the ratio of 3:4:5. Find the measure of an inscribed angle that intercepts the largest arc.

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Patricky · Answer 1

If the ratio is 3:4:5 it's good to know what the ratio of one of those three to the total is.

3+4+5 = 12.

So the "3" in 3:4:5 is actually 3/12th of a circle (that's 1/4th, a quarter!).

What about the largest part?

The "5" in 3:4:5 is actually 5/12th of a circle!

We know a circle has a total of 360 degrees.

We need 5/12th of that.

So we mulitply: 360 * 5/12 = 150 degrees.