Hình 7A1 Tính góc Bài 5 #toan7

Input for triangle ABC Triangle ABC has an internal angle bisector AD which means that angle A1 is equal to angle A2 and it has an external angle bisector AE That means angle A3 is equal to angle A4 The difference between angle B and angle C is 30 degrees meaning angle B is 30 degrees larger than angle C The requirement is to calculate angle ADB Angle ADB is angle D1 And angle AEB is angle E this So what does this problem give us Find the angle between the internal and external angle bisectors of a triangle At the same time the difference between angles B and C is 30 degrees Require to find angle ADB Angle D1 And angle AEB which is angle E Okay To make it easier let's use the notation Assigning angles to make it easier to read right That is we will label the angles D1 D2 A1 A2 A3 A4 Is that okay What do we know about these D1 and D2 angles What do we know about these D1 and D2 angles This is a pair of adjacent supplementary angles So these are two angles that add up to 180 degrees right But they asked to calculate one angle Kem knew that To find two numbers when knowing their sum and difference is very easy to figure out isn 't it Because the larger number is equal to the sum plus the difference divided by two The smaller number is equal to the sum minus the difference of the two numbers Now we have the sum Therefore it is natural in thinking That is we will ask the question There The total is 180 The difference is 30 So it's very simple So we get that angle right Total is 180 Difference is 30 Then what is the larger angle What is the larger angle The large number is equal to Total That is We have D1 plus D2 D2 plus D1 By 180 Then now we have Then now we ask the question What is D2 minus D1 What is D2 minus D1 Yes What is D2 minus D1 We have Is D1 equivalent to C plus A2 Then it is equal to angle A2 plus angle C This is the exterior angle of the triangle And D2 is equal to angle A1 plus angle B right That is Then We will have it Here we will write it out That is D2 D2 minus D2 equals C Add A2 to D2 equals C plus A2 D1 is equal to D2 is equal to B plus A1 I thought this place was D1 D1 is equal to C Triangle angle A2 is at the outer corner Angle D1 is equal to angle C plus angle A2 Angle D2 is equal to angle A1 plus angle B Then by angle A1 plus angle B We have angle B plus angle A1 That Well then now I take This D2 corner I subtract this D1 corner Then are A1 and A2 equal A1 and A2 are equal So take the one below the letter above Then it is equal to angle B and angle C Therefore The question tha What is D2 equal to This What is D2 equal to Then in this case we answer as follows: What is D2 the D1 It is the angle B the angle C Here it is I take the one below the letter above right But the A1 and the A2 are equal This is the angle bisector so they are equal So by B letter C Then by By 30 degrees Change to B letter C by 30 degrees Then These are two numbers whose sum is 180 and whose difference is 30 Then what is the measure of each angle Find two numbers given the correct sum and difference The larger number is the sum plus the difference divided by 2 The smaller number is the sum minus the difference divided by 2 Therefore our D2 is It is 180 plus 30 divided by 2 Itis105 D1 is still there What is it worth 75 right D1 is 75 degrees Through this situation What do we learn about the aspect of thinking The aspect of thinking To calculate angle people usually consider the relationship of that angle with the other angle with the remaining angles right It can no longer be considered in isolation For example the calculation of D1 In this case we can calculate the sum and difference of D1 and D2 We calculated the sum D1 and D2 A factor It never exists in isolation It is always connected to elements that are related to it Isn't that right We are the same we also have connections For others Beside me Maybe dry maybe deep but they all have a connection I've only just met them So we should all cherish the relationships around us Now let's move on to question 2 Now to calculate the angle to calculate this angle E we will rely on triangle ABE Because this angle E now has only one relationship Which we see is within the triangle ABE Isn't that right Here we have angle B as the exterior angle Angle B is the exterior angle Therefore we have that angle B will be equal to angle E Plus angle A3 Then on the other hand we have AE as the external angle bisector of the angle This AE is the external angle bisector of angle ABC What do we have then So we have that The corner This A3 corner twice It is the external angle It is the external angle of triangle ABC The external angle of this triangle ABC is equal to the sum of the two internal angles It is adjacent to angle B and angle C Therefore combining with the above I will get That is What will I get Combined with the thing that Angle E is equal to angle A3 Ah E plus A3 is equal to angle B There it is Now teacher write it down We have First angle B Angle B is equal to angle E With angle A3 Second is twice the angle twice the angle A3 This angle A3 is the same as angle A So it is equal to angle B plus angle C right Twice A3 will be equal to B plus C B plus C Then Then let's do it this way I'll figure it out Now I combine these two things What will I get What will I get by combining the two above By removing this A3 okay By us removing this A3 Then In these two relationships we will obtain Calculating E according to B and C immediately I eliminate these two and then I can calculate E using B and C How do I eliminate them Then I can Here for example I can multiply by 2 here Multiply by 2 here Then I add them up What will be gained then Here we will multiply by 2 here Multiply by 2 here Then add them up So when combined these two right Do we eliminate them all Let's eliminate these two as well Let 's also eliminate this corner B So here will be angle B Corner B By twice the angle E Is the corner C correct What does this mean It means that angle E will be equal to Angle B minus angle C Then divide by 2 But B minus C is 30 degrees right So this one is 15 degrees We get E as 15 degrees Thus we have obtained A very beautiful result regarding the relationship Between angle D and angle E with angles B and C I obtained the relationship between angle D and angle E with angles B and angle C This result is for you to pay attention to in order to apply it During the process of doing exercises learning is a very long process It's about accumulating knowledge but also about practicing thinking and skills so that I become more proficient every day