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Inscribed triangle in circle missing an angle

This math skill involves calculating a missing angle in an inscribed triangle within a circle. It covers the relationship between inscribed angles and central angles, specifically noting that an inscribed angle is half of its corresponding central angle when the triangle's side is a diameter. It also utilizes the property that the sum of angles in a triangle is 180 degrees.

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Teaching Transcript

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What is the missing angle on this inscribed triangle in this circle?

When we have an inscribed angle and a central angle from the same points, the inscribed angle is half the central angle. So, since this is a diameter, our inscribed angle will be half of 180, or 90 degrees.

Now we can use the fact that the inside angles of a triangle must add up to 180 degrees

So our missing angle is 30 degrees

Skill Practice

Inscribed triangle in circle missing an angle

Test your understanding of inscribed triangle in circle missing an angle by practicing it! Work through the below exercises to use it in practice.