1) The value of the missing variables x and y are; y = 21°, x = 45°
2) The value of the variable x and the angle are; x = 6 and ∠ABC = 108°
3) Supplement of 51° is 129°
Complement of 51° is 39°
How to find missing angles?
1) We know that sum of angles on a straight line is 180°.
We see that ∠QNP and ∠QNM form a straight line and so;
∠QNP + ∠QNM = 180°
3y + 34 + 4y - 1 = 180
7y = 180 - 33
7y = 147
y = 21°
Similarly;
3x - 52 + 2x + 7 = 180
5x - 45 = 180
5x = 225
x = 225/5
x = 45°
2) We are told that the line BD bisects ∠ABC where;
m∠ABD = 9x°
m∠DBC = (4x + 30)°
Thus;
9x = (4x + 30)°
9x - 4x = 30
5x = 30
x = 30/5
x = 6
Thus;
∠ABC = 9(6) + (4(6) + 30)°
∠ABC = 108°
3) We are given the angle as 51°.
Now, supplementary angles sum up to 180° while complementary angles sum up to 90°. Thus;
Supplement = 180 - 51 = 129°
Complement = 90 - 51 - 39°
Read more about Missing angles at; https://brainly.com/question/28293784
#SPJ1
