Can someone explain this to me? I was absent today and my teacher isn’t helping.

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  1. adjacent: ACB, BCD and BCD, DCE. vertical: ACB, DCE and BCD, ECA

  2. adjacent: KGJ, JGI and HGM, MGK. vertical: JGI, MGL and HGM, KGJ

  3. adjacent. x = 49°

  4. adjacent. x = 71°

Step-by-step explanation:

As I noted in the attachment, vertical angles are formed from opposite rays (lines that cross). They share only a vertex. Each of the crossing lines makes up one side of each of the vertical angles. (You can think of each line as being made of opposite rays from the vertex of the angle.)

Adjacent angles share both a vertex and one side. (They do not overlap.) For example, in Figure 2, angles KGM and LGM are not adjacent, even though they share verex G and side GM. This is because they overlap. In that figure, angles KGL and LGM are adjacent angles.

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1. To identify adjacent angles, choose a ray and make note of the angles on either side of it.

  adjacent: {ACE, ACB}, or {BCA, BCD}, or {DCB, DCE}, or {ECD, ECA}

To identify vertical angles, choose two crossing lines and one of the 4 spaces between them. The other vertical angle will be non-adjacent, in the opposite space of the same size.

  vertical: {ACB, ECD}, or {ACE, BCD}

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2. adjacent: any of the pairs {KGJ, JGI}, {JGI, IGH}, {IGH, HGM}, {HGM, MGL}, {MGL, LGK}, {LGK, KGJ}.

Note that these are the nearest, smallest pairs of adjacent angles. This is usually what we are talking about when we refer to adjacent angles. We could add to the list pairs like {IGH, IGK}, {IGM, IGL}.

 vertical: (lines IL, HK) {IGH, LGK} or {IGK, LGH}; (lines IL, MJ) {IGM, LGJ} or {IGJ, MGL}; (lines HK, MJ) {HGM, KGJ} or {HGJ, KGM}

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3. The angles share a ray, so are adjacent. Together, they make up a right angle, so they are complementary.

  x = 90° -41°

  x = 49°

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4. The angle share a ray, so are adjacent. Together, they make up a linear angle, so are supplementary.

  x = 180° -109°

  x = 71°

d is the answer

step-by-step explanation: