in each of the following relationships among marked angles are given below the figure. find the measures of the marked angles
a. m(<DOC)=3?4m(<BOA)
b. m(<AOB)is 30 less than 2?m(BOC)
c, m(<AOB)-m(<BOC)=50
To find the measures of the marked angles in each of the given relationships, you need to set up equations and solve them. Let's go through each relationship one by one:
a) Given: m(<DOC) = (3/4)m(<BOA)
To find the measure of the marked angle <DOC, we need to find the measure of <BOA first. Let's assume the measure of <BOA is x degrees.
So, m(<BOA) = x
Then, according to the given relationship, we have:
m(<DOC) = (3/4)x
Therefore, we now know the measure of <DOC is (3/4)x degrees.
b) Given: m(<AOB) is 30 less than 2 times m(<BOC)
To find the measure of the marked angle <AOB, we need to find the measure of <BOC first. Let's assume the measure of <BOC is y degrees.
So, m(<BOC) = y
Then, according to the given relationship, we have:
m(<AOB) = 2m(<BOC) - 30
Therefore, we now know the measure of <AOB is (2y - 30) degrees.
c) Given: m(<AOB) - m(<BOC) = 50
To find the measure of the marked angle <AOB, we need to find the measure of <BOC first. Let's assume the measure of <BOC is z degrees.
So, m(<BOC) = z
Then, according to the given relationship, we have:
m(<AOB) = z + 50
Therefore, we now know the measure of <AOB is (z + 50) degrees.
Note: In each case, we assume the measure of one angle and use that to find the measure of the other angle based on the given relationship.