Beam OD drawn from the top of the unfolded angle AOB divides it into angles AOD and BOD

| March 18, 2021 | education

Beam OD drawn from the top of the unfolded angle AOB divides it into angles AOD and BOD, the ratio of the degree measures of which is 5: 4. find the degree measure of the angles AOD and DOB.

Let’s introduce the notation for the angles AOD and BOD:

Let x be one piece, then the AOD angle is 5x and the BOD angle is 4x.

Let’s find what one part is equal to:

Since the degree measure of the expanded angle AOB is equal to 180 and the angle AOB is equal to the sum of the angles AOD and BOD, then we compose and solve the equation:

5x + 4x = 180,

9x = 180,

x = 180: 9,

x = 20.

One part is equal to 20.

Let’s find the degree measure of the angle AOD:

5 * 20 = 100.

Determine the degree measure of the BOD angle:

4 * 20 = 80.

Answer: The degree measure of the AOD angle is 100, and the degree measure of the BOD angle is 80.



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