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tonb

Answer:

∠BAD = 100°

∠ADC = 105°

∠DCB = 50°

∠ABC = 105°

Step-by-step explanation:

∠BAD is given.

∠ADC is supplementary to the 75°, so it is 180-75 = 105°

∠DCB is 50° just like its opposite angle

The sum of all angles in a quadrilateral must be 360, so ∠ABC = 360-100-105-50 = 105.
Angle BAD = 100 degrees (vertically opposite)
Angle ADC = 75 degrees (vertically opposite)
Angle DCB = 130 ( 180-50= 130, angles in a straight line add up to 180 degrees)
Angle CBA=
75+75 = 150
360-150 = 210 (angles around a point add up to 360 degrees)
210/2= 105 (divide by two to find the size of one angle)
So,
105+100+50 = 255
Angles inside a quadrilateral add up to 360
360-255= 105
Angle CBA =105

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