 In this question, it's given that the sum of two angles of a triangle is equal to its third angle and We have been asked to determine the measure of the third angle. Okay, so let's first draw the diagram So, let us say This is my triangle. Okay, so triangle is a BC let's say, okay, what is given guys the sum of two angles of a triangle is equal to its third angle, so a Solution right so angle a plus angle B. Let's say is equal to angle C Right determine the measure of the third angle. So we have to measure the Find the value of this angle angle C now by angle some property by angle some Property of a tank triangle Property of a triangle, what do we know? Angle a plus angle B plus angle C is 180 degrees Right, but angle a plus B is angle C. So this is equal to angle C from here So that means I can write angle C plus angle C is 180 degrees that means twice angle C is 180 degrees That means angle C is equal to 180 degrees by 2 Which is 90 degrees now don't go by the figure which I have drawn So while we were solving the question, we didn't know the value So hence clearly angle C doesn't look like a 90 degrees, but then that was just a representative diagram So hence the solution is angle C is 90 degree Correct in the same problem, let's say if they say that you know angle a is 30 degrees Let's say if they say that angle a is 30 degrees if If let's say if this information is given then you can find out angle B as well. So angle B will be how much? 90 minus 30 that is 60 degrees Correct, isn't it? So angle B will be 60 degrees if angle a is 30 Why because a plus B was 90 which was equal to angle C, right? So this is the solution to this problem Now in this question, it's given that of the three angles of a triangle One is twice the smallest and another is twice times three times the smallest We have to find the angles. So let's first draw a representative diagram. So let's say this is my triangle a, b, c, a b C right and let's say one of the three angles of a triangle One of the three angles of a triangle one is twice the smallest. Let's say C is The smallest one C angle C is smallest one and let us Assume it to be x degrees. Okay. So one is twice the smallest. That means let's say angle a is equal to twice angle C that is 2x and The other is twice the smallest. So angle B is equal to 3. This is the smallest So 3x. So what is the assumption assuming? Assuming what assuming angle C to be the smallest To be the smallest angle, right? Anyone you could have taken as smallest. There is no problem. So I have taken a C just Just like that. So there is no a problem if you consider a or B as smallest the problem will not change now So, what do I know now then clearly angle a plus angle B plus angle C is 180 degrees. Why is this because of angle? some property Property of a Triangle right now some of three angles in a triangle is 180 degrees. Isn't it? So angle a was 2x angle B was 3x and angle C was x and This total is 180 degrees So that means if you see 2x plus 3x plus x which is 6x is equal to 180 degrees So clearly x will be 1 8 0 divide by 6 which is 30 degrees. Isn't it guys? So what do we observe that the smallest angle was x which is 30 degrees, right? So hence smallest angle is smallest angle Is equal to 30 degrees. This is a solution