Final answer:
The valid equation under the angle addition postulate is c) m∠deg + m∠gef = m∠def, which states that the sum of adjacent angles equals the measure of the larger angle they create.
Step-by-step explanation:
Under the angle addition postulate, the valid equation is c) m∠deg + m∠gef = m∠def. According to the postulate, if a point E lies inside the interior of ∠DEF, the measure of ∠DEG plus the measure of ∠GEF equals the measure of the entire ∠DEF. This principle can be applied to understand how larger angles are constructed from the sum of smaller adjacent angles. None of the other provided equations satisfy the angle addition postulate; angles aren't combined using multiplication, and there's no indication that ∠DEF has twice the measure of ∠GEF without more context about the relationship between these angles.
The Angle Addition Postulate states that the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together. The formula for the postulate is that if D is in the interior of
ABC then
ABD +
DBC =
ABC. Adjacent angles are two angles that share a common ray. When identifying an angle, there are up to three possible ways to name it. The vertex is a crucial component to an angle's name. Angles can be named by only their vertex point or by using three points that make the angle in which the vertex must be the middle point. Angles can also be labeled with numbers to make identification easier. The three possible ways are not always options to name angles, such as adjacent angles that share a vertex. The Angle Addition Postulate states that the sum of two adjacent angle measures will be equal to the measure of the larger angle they form.