Question

solve the challenge
enter the unknown angle measures into the table.
press \check my work\ when you are finished.
use the sketch tool if it helps to illustrate your thinking.
some of your measures are incorrect. please try again.
angle measure (degrees)
abc 29
abd 154
abe 151
dbe 28
gbe 29
dbg 26

Explanation:

Step1: Recall angle - addition postulate

Angles around a point sum to 360 degrees. Also, linear - pair angles sum to 180 degrees.

Step2: Analyze linear - pair relationships

For example, if we consider a linear pair, say \(\angle ABC\) and \(\angle ABD\), since they form a straight - line, \(\angle ABC+\angle ABD = 180^{\circ}\). Given \(\angle ABC = 29^{\circ}\), then \(\angle ABD=180 - 29=151^{\circ}\).

Step3: Use angle - subtraction

If \(\angle ABE = 151^{\circ}\) and \(\angle ABC = 29^{\circ}\), then \(\angle CBE=\angle ABE-\angle ABC = 151 - 29 = 122^{\circ}\). If \(\angle DBE = 28^{\circ}\), and we know \(\angle ABE = 151^{\circ}\), we can check the relationships. Also, if \(\angle GBE = 29^{\circ}\) and \(\angle DBE = 28^{\circ}\), then \(\angle DBG=\angle GBE-\angle DBE=29 - 28 = 1^{\circ}\).

Answer:

Angle	Measure (degrees)
ABD	151
ABE	151
DBE	28
GBE	29
DBG	1