Question

Line OC is the angle bisector of angle AOB, and line OD is the angle bisector of angle COB. If m(∠ AOC) = 3y-4 and m(∠ COD) = 28, then find the value of (y).

a) 12
b) 16
c) 14
d) 10

Answer 1

We use the properties of angle bisectors to set up an equation involving the measure of the angles and solve for y. The calculation shows that y equals 16.

Step-by-step explanation:

The student is asked to find the value of y in a geometry problem involving angle bisectors. Since line OC is the bisector of angle AOB and line OD is the bisector of angle COB, we can set up the problem using the given angle measures. Angle AOC is given as 3y - 4 and angle COD is given as 28 degrees.

Because OD is the bisector of angle COB, the measure of angle COB is twice that of angle COD, so COB is 56 degrees. The angles AOC and COB together form angle AOB. Therefore, by setting the sum of angles AOC and COB equal to angle AOB and solving for y, we can find its value.

The equation becomes 3y - 4 + 56 = 2(3y - 4) as angle AOB is twice the measure of angle AOC. Simplify the equation to find y. Solving for y yields the answer:

y = 16