In each of the following, relationships among marked angles are given below the figure. Find the measures of the marked angles.
DOC = 3/4m( COB =
BOA =
COB = m( COA =
BOA =
To find the measures of the marked angles, we need to use the given relationships among the angles in the figure.
Let's start with the first set of relationships:
1. DOC = 3/4m (where m denotes the measure of an angle)
2. COB = ?
From the first relationship, we know that DOC is equal to 3/4 times the measure of COB. So, if we have the measure of COB, we can find the measure of DOC.
To find COB, we can use the fact that the sum of angles in a triangle is 180 degrees. Since DOC and COB are angles in the triangle COB, we have:
DOC + COB + (180 - m) = 180
From the given relationship, we know that DOC = 3/4m. Substituting this into the equation, we get:
3/4m + COB + (180 - m) = 180
By rearranging the equation, we find:
COB = m/4
Now, let's move to the second set of relationships:
1. COB = m
2. BOA = ?
From the first relationship, we know that COB is equal to the measure of BOA. So, if we have the measure of COB, we can find the measure of BOA.
To find the measure of BOA, we can directly substitute COB's measure into BOA:
BOA = m
Therefore, the measures of the marked angles are:
- DOC = 3/4m
- COB = m/4
- BOA = m