Inside the swept angle AOB, two beams OD and OC are drawn so that the angle AOC

Inside the swept angle AOB, two beams OD and OC are drawn so that the angle AOC = 130 ° and the angle DOB = 120 °. Find the corner DOC.

A flattened angle is an angle whose sides are on the same straight line.

The measured angle of the flattened angle is 180º, so the angle AOB = 180º.

Consider the drawing. Angle AOB can be thought of as the sum of two angles.

angle AOB = angle AOC + angle COB

Let’s express the COB angle.

COB angle = AOB angle – AOC angle

Substitute the numerical values.

angle COB = 180º – 130 ° = 50º

Also, the AOB angle can be thought of as the sum of the other two angles.

AOB angle = AOD angle + DOB angle

Let’s express the angle AOD.

angle AOD = angle AOB – angle DOB

angle AOD = 180º – 120 ° = 60 °

Now imagine the angle AOB as the sum of three angles.

AOB angle = AOD angle + DOC angle + COB angle

Let’s express the angle DOC.

DOC angle = AOB angle – AOD angle – COB angle

angle DOC = 180º – 60 ° – 50º = 70º

Answer: angle DOC = 70º