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Q4
Let the point where line AB and line CD intersect be O
Since AB and CD are straight lines, angle AOC = angle BOD
Angle e = angle AOC = 30 degrees
Since AB is a straight line, angle AOB = 180 degrees
angle f = angle AOB - 50 - 90 - angle e
angle f = 180 - 50 - 90 - 30
angle f = 10 degrees
Let the point where line AB and line CD intersect be O
Since AB and CD are straight lines, angle AOC = angle BOD
Angle e = angle AOC = 30 degrees
Since AB is a straight line, angle AOB = 180 degrees
angle f = angle AOB - 50 - 90 - angle e
angle f = 180 - 50 - 90 - 30
angle f = 10 degrees
How to know that it is not angles and a point or adj angles??
Sorry I don't understand your question. Do you understand my working? To clarify further, in Mathematics there are more than 1 solution to solve a particular problem, some shorter than others, some easier to understand.
Because some questions also have angles at a point and some others have adj angles so how to know if it's one of them?
This is based on experience and practice, as stated there is no fixed way of solving a question, sometimes both methods can be used. There is no "perfect" or "right" method, as long as you arrive at the answer using a suitable method.
Q5
angle YOB = angle YOX - angle BOX
angle YOB = 90 - 56
angle YOB = 34
angle COY = angle COB - angle YOB
angle COY = 90 - 34
angle COY = 56 degrees
Since line AB and line WX are straight lines, angle BOX = angle WOA = 56
angle AOX = 180 - 56
angle AOX = 124 degrees
(since line WX is a straight line, angle WOX = 180)
angle YOB = angle YOX - angle BOX
angle YOB = 90 - 56
angle YOB = 34
angle COY = angle COB - angle YOB
angle COY = 90 - 34
angle COY = 56 degrees
Since line AB and line WX are straight lines, angle BOX = angle WOA = 56
angle AOX = 180 - 56
angle AOX = 124 degrees
(since line WX is a straight line, angle WOX = 180)
Can write the reasons? Ty