Answer:
Step-by-step explanation: Hello!
To find angle EOD, you are already given two angle measurements. The measure of angle AOB is 55 degrees and the measure of angle BOC is 30 degrees. The important thing that you have to remember to solve this problem is that vertical angles are congruent. (I won't be explaining the definition of vertical angles, but you can find a lot of images and explanations online). This means the two angles formed by two lines intersecting each other in any way is always congruent. Angles AOB and EOD are congruent by the definition of vertical angles. This means that the measure of angle EOD is 55 degrees.
Now, you have to find the measurement of angle DOC. By the definition of straight lines, you know that the angles formed by a straight line all add up to 180 degrees. This means that:
EOD + DOC + COB = 180 degrees. You are already given two of these measurements. (Angle EOD which you just figured out and Angle COB which was already given). Fill these numbers in the equation.
55 + DOC + 30 = 180. Combine like terms (55 + 30)
85 + DOC = 180. Then subtract 85 from both sides using the subtraction property of equality.
(85 - 85) + DOC = (180 - 85)
DOC = 95.
The measure of angle DOC = 95.
You can check this by substituting the new measurement for angle DOC back into the equation.
Does 55 + 30 + 95 = 180?
85 + 95 = 180
180 = 180.
The measure of angle DOC is 95 degrees and the measure of angle EOD is 55 degrees.