The sides xy and xz of a triangle xyz are produced from points A and B respectively, if angle Ayz equals 105 degrees and angle Bzy is twice angle yxz. find the value of the angle.

what do you mean by "produced"? Are A and B both external to xya, or what? This is all just a bit vague.

please the answer is needed urgently.thanks

A and B are external

To find the value of angle YXZ, we need to use the information given in the problem. Let's break down the steps to solve it:

1. Draw a triangle XYZ with points A and B as specified.

2. The angle AYZ is given as 105 degrees. Mark it on the diagram.

3. The angle BZY is stated to be twice the angle YXZ. Let's use a variable to represent the angle YXZ. Let's say angle YXZ is equal to "x" degrees.

4. Therefore, angle BZY is equal to 2x degrees. Mark angle BZY on the diagram.

5. Since we have two angles now (105 degrees and 2x degrees), we can find the third angle, angle XYZ, since the sum of the angles in a triangle is 180 degrees.

6. The sum of the three angles in the triangle XYZ is 105 degrees (angle AYZ) + 2x degrees (angle BZY) + angle XYZ.

Therefore, 105 + 2x + angle XYZ = 180.

7. Now, rearrange the equation to solve for angle XYZ:

angle XYZ = 180 - 105 - 2x.

Simplifying further: angle XYZ = 75 - 2x.

This equation gives us the value of angle XYZ in terms of "x".

8. We need to remember that the sum of all angles in a triangle is 180 degrees. Therefore, angle XYZ can't be negative. Since we're looking for a positive angle, set the expression 75 - 2x greater than zero and solve for "x".

75 - 2x > 0.

Add 2x to both sides: 75 > 2x.

Divide by 2 on both sides: 37.5 > x.

Therefore, x is greater than 37.5.

9. Now substitute the value of "x" back into the equation angle XYZ = 75 - 2x to find the value of angle XYZ:

angle XYZ = 75 - 2(37.5).

Simplifying further: angle XYZ = 75 - 75 = 0 degrees.

So, the value of angle XYZ is 0 degrees.

Therefore, the value of angle YXZ is 0 degrees.