HU
is tangent to circle OO at point HH, and H, M, with, left-right arrow, on top
HM
is a secant line. If m, arc, H, M, equals, 108, degreesm
HM
⌢
=108
∘
, find m, angle, M, H, Um∠MHU.
Since HM is a secant line that intersects circle OO and arc HM is 108 degrees, we can use the Inscribed Angle Theorem.
The Inscribed Angle Theorem states that an angle inscribed in a circle is equal to half the measure of the arc it intercepts.
Therefore, we have:
m∠MHU = 1/2 * m(arc HM)
m∠MHU = 1/2 * 108
m∠MHU = 54 degrees
Therefore, the measure of angle MHU is 54 degrees.