Question

5.) In each of the following, relationships among marked angles are given below the figure. Find the measures of the marked angles.

Answer 1

the three angles are supplementary angles. .

therefor use the formula.

A+B+C =180
120+3/4B+B =180
B =34.29
3/4B = 25.71

therefore, the three angles are 120, 34.29 and 25.71

Answer 2

All of these angles together are supplementary, meaning they add up to 180 degrees, so if one angle is 120, then the other two have to add up to 60 degrees.
x = measure of angle DOC
y = measure of angle BOA
we can use a systems of equations now
x = 3/4y
x + y = 60 so y = 60 - x
Use substitution
x = 3/4(60 - x)
x = 45 - 3/4x
7/4x = 45
x is approximately 25.7 degrees.
x + y = 60
25.7 + y = 60
y = 34.3

Answer 3

oh wait I think i see it, sorry i'm blind

Answer 4

They are the same but he just skipped a step and made it one equation with one variable.

Answer 5

thank you both!

Answer 6

glad to help. .