Question Video: Finding the Measure of a Central Angle Using the Properties of Radii Mathematics

Find π‘šβˆ π΄π‘€π΅.

01:44

Video Transcript

Find the measure of angle 𝐴𝑀𝐡.

Angle 𝐴𝑀𝐡 is the angle formed when we travel from 𝐴 to 𝑀 to 𝐡. So that’s the angle that I’ve marked in orange on the diagram. We can see that this angle is inside a triangle which has two of its corners on the circumference of a circle. Its third corner is at the center of the circle, the point 𝑀.

This means that the lines 𝐴𝑀 and 𝐡𝑀 are each radii of the circle as they connect a point on the circumference to the center 𝑀. This also means that 𝐴𝑀 and 𝐡𝑀 are equal in length.

In turn, this tells us that triangle 𝐴𝑀𝐡 is an isosceles triangle as it has two equal sides. In an isosceles triangle, the base angles are also equal. So those are the angles formed by the equal sides and the third side. In this case, that’s angle 𝑀𝐴𝐡 and angle 𝑀𝐡𝐴.

We already know that the measure of angle 𝑀𝐴𝐡 is 27 degrees as this was given on the diagram. So now we know that the measure of angle 𝑀𝐡𝐴 is also 27 degrees. To find the measure of the third angle in this triangle, we can apply the rule that the angle sum in any triangle is 180 degrees.

So the measure of angle 𝐴𝑀𝐡 is 180 degrees minus the measures of the other two angles which are each 27 degrees. Subtracting two lots of 27 from 180 gives 126.

So the measure of angle 𝐴𝑀𝐡 is 126 degrees.

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