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In the figure, M is a circle where the measure of B = 55° and AB = CD. Find the measure of the central angie subtended by minor arc CD.

In the figure M is a circle where the measure of B 55 and AB CD Find the measure of the central angie subtended by minor arc CD class=

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anbu40

Answer:

A) 70°

Step-by-step explanation:

To find the central angle (∠CMD) subtended by minor arc CD:

In ΔABM,

AM = BM  (radius) ⇒ΔABM is isosceles triangle.

       ∠BAM = ∠ABM   {Angles opposite to equal sides are equal}

       ∠BAM  = 55°

∠AMB + ∠ABM + ∠BAM = 180   {Angle sum property}

∠AMB + 55 + 55 = 180

       ∠AMB + 110 = 180

                ∠AMB = 180 - 110

                ∠AMB = 70°

It is given that AB = CD. Equal chords subtend equal angles at the center.      

∠CMD =∠AMB

      [tex]\boxed{\bf \angle CMD = 70^\circ}[/tex]