Question

Points C and D divide the semicircle into three equal parts. Match the angles with their measures.

∠CAE
A. ∠CAD
B. ∠BAE
C. ∠DEC
D. 15°
E. 30°
F. 60°
G. 120°
H. 180°

Answer 1

∠CAE = 120°
∠CAD = 60°
∠BAE = 180°
∠DEC = 30°

We start out with the fact that points C and D split the semicircle into 3 sections.  This means that ∠BAC, ∠CAD and ∠DAE are all 60° (180/3 = 60).

Since it forms a straight line, ∠BAE is 180°.

Since it is formed by ∠CAD and ∠DAE, ∠CAE = 60+60 = 120°.

We know that an inscribed angle is 1/2 of the corresponding arc; since CD is 1/3 of the circle, it is 1/3(180) = 60; and this means that ∠DEC = 30°.

Answer 2

If this person is correct then it should look like this if you have Plato

your welcome ;0 =)