 Hello students, let's work out the following problem. It says in triangle A, B, C, angle A is x degrees, angle C is y degrees, angle B is 3x minus 2 degrees. Also angle C minus angle B is 9 degrees. Find the three angles. So let's now move on to the solution. Now we know that in a triangle, sum of three angles is 180 degrees. So we have angle A plus angle B plus angle C is equal to 180 degrees. Now angle A is x degrees, angle B is 3x minus 2 degrees plus angle C which is y degrees is equal to 180 degrees. So we have x plus 3x minus 2 plus y is equal to 180. Now x plus 3x is 4x plus y is equal to 180 minus 2 plus 2. Since we transpose, the sign will change. So we have 4x plus y is equal to 182. Let's name this as 1. Also we are given that angle C minus angle B is 9 degrees. Now angle C is y degrees, angle B is 3x minus 2 degrees is equal to 9 degrees. So this implies y minus. Now since we have negative sign outside the bracket, when we will open the bracket, sign will change. So it becomes minus 3x plus 2 is equal to 9. So again we have y minus 3x is equal to 9 minus 2. So this implies y minus 3x is equal to 7. Taking negative sign common, we have 3x minus y is equal to minus 7. Let's name this as 2. Now we'll solve these two equations for x and y. So add equation 1 and 2. Equation 1 is 4x plus y is equal to 182. Equation 2 is 3x minus y is equal to minus 7. Now we add 2 equation. 4x plus 3x is 7x plus y gets cancelled with minus y. 182 minus 7 is 175. So this implies x is equal to 175 divided by 7. That is 25. Now to get the value of y, we'll put value of x in any of the two equations. So we'll put x is equal to 25 in equation 2. So 3 into 25 minus y is equal to minus 7. 3 into 25 is 75 minus y is equal to minus 7. So this implies minus y is equal to minus 7 minus 75. So this implies minus y is equal to minus 82. Canceling negative signs on both sides, we have y is equal to 82. So angle A is given to be x degrees. So it is 25 degrees. Angle B is 3x minus 2 degrees. That is 3 into 25 minus 2 degrees. That is 75 minus 2 degrees. That is 73 degrees. And angle C is y degrees. And y is 82. So we have angle A as 25 degrees. Angle B as 73 degrees. Angle C as 82 degrees. So this completes the question and the session. Bye for now. Take care. Have a good day.