In triangle ABC, angle C = 61; AD-bisector A; angle wad is 40. find the degree measure BDA.

1) First, find the value of the angle BAC.
By convention, AD is a bisector.
So AD bisects the BAC angle.
Hence, it can be written for the BAC angle.
BAC = BAD + CAD.
And since the BAD angle is equal to the CAD angle, we will write the following equality.
BAC = 2BAD.
By convention, the BAD angle is 40 °.
BAC = 2BAD.
BAC = 2 × 40 °.
BAC = 80 °.
2.) Now let’s find the value of the angle B.
According to the rule, the sum of the values ​​of all the angles of any triangle is 180 °.
Now let’s draw up an equality for triangle ABC.
In this case, we take into account that the angle A in the triangle ABC is also the angle BAC.
A = BAC = 80 °.
A + B + C = 180 °.
B + 80 ° + 61 ° = 180 °.
B + 141 ° = 180 °.
B = 180 ° – 141 °.
B = 39 °.
3.) Now we find the degree measure of the angle BDA.
In this case, for convenience, we write the angle BDA as angle D.
Next, we write down the sum of the angles of the triangle ABD.
In this case, we will take into account that the angle BAD and angle A are the same angle of the triangle ABD.
BAD = A = 40 °.
A + B + D = 180 °.
40 ° + 39 ° + D = 180 °.
79 ° + D = 180 °.
D = 180 ° – 79 °.
D = 101 °.
Answer: 101 °.