Video Transcript
Find the measure of angle
𝐴𝑀𝐵.
Angle 𝐴𝑀𝐵 is the angle formed
when we travel from 𝐴 to 𝑀 to 𝐵. 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
𝐵𝑀 are each radii of the circle as they connect a point on the circumference to
the center 𝑀. This also means that 𝐴𝑀 and 𝐵𝑀
are equal in length.
In turn, this tells us that
triangle 𝐴𝑀𝐵 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 𝑀𝐴𝐵
and angle 𝑀𝐵𝐴.
We already know that the measure of
angle 𝑀𝐴𝐵 is 27 degrees as this was given on the diagram. So now we know that the measure of
angle 𝑀𝐵𝐴 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 𝐴𝑀𝐵 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 𝐴𝑀𝐵 is
126 degrees.
