Given CircleDot E with diameter BDbar finish the following b

Given CircleDot E with diameter BD^bar, finish the following by writing numbers in the blanks. angle ______ is a central angle. angle ________ and angle _________ are inscribed angles that both intercept AB^OverParenthesis. m angle 2 = _______ sdot mAB^OverParenthesis by Theorem ________. angle 3 TildeFullEqual angle 2 by Theorem ______. m angle 2 = ________ sdot m angle 1, so m angle 1 = ________ sdot m angle 3.

Solution

m(1) is the central angle. m(2) and m(3) are inscribed angles that both intercept arc AB. m(2) = 1/2 * m(arc AB) by theorem of inscribed angles. m(3)=m(2) by theorem that states angles inscribed by the same arc are equal.
m(2) = 1/2*m(1), so from the above step m(1) = 2*m(3).

Major point to note is that Inscribed angle is half of the central angle.