Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.
points c and d divide the semicircle into three equal parts. match the angles with their measures.
15° ∠cae 30° ∠cad 60° ∠bae 120°
∠dec 180°

Explanation:

Step1: Find arc measures

A semicircle is $180^\circ$. Split into 3 equal arcs: $\frac{180^\circ}{3}=60^\circ$, so $\overset{\frown}{BC}=\overset{\frown}{CD}=\overset{\frown}{DE}=60^\circ$

Step2: Calculate $\angle CAD$

$\angle CAD$ is inscribed over $\overset{\frown}{CD}$: $\angle CAD=\frac{1}{2}\times60^\circ=30^\circ$

Step3: Calculate $\angle CAE$

$\angle CAE$ is half of $\angle CAD$ (symmetry): $\angle CAE=\frac{1}{2}\times30^\circ=15^\circ$

Step4: Identify $\angle BAE$

$\angle BAE$ is a straight angle: $\angle BAE=180^\circ$

Step5: Calculate $\angle DEC$

$\angle DEC$ subtends $\overset{\frown}{DCB}$: $\overset{\frown}{DCB}=60^\circ+60^\circ=120^\circ$, so $\angle DEC=\frac{1}{2}\times(180^\circ+60^\circ)=120^\circ$

Answer:

$\angle CAE \longleftrightarrow 15^\circ$
$\angle CAD \longleftrightarrow 30^\circ$
$\angle BAE \longleftrightarrow 180^\circ$
$\angle DEC \longleftrightarrow 120^\circ$