Answer:
Qn 6:
Adjacent angles on a straight line always add up to 180°
∠ABD + ∠DBC = 180
(10x +1) + (9x-11) = 180
19x - 10 = 180
19x = 190
x = 10
Subt x = 10 into ∠ABD and ∠DBC
∠ABD = 10(10) + 1 = 101°
∠DBC = 9(10) - 11 = 79°
Qn 7:
Adjacent angles on a straight line always add up to 180°.
Since ∠CBE = 90°, ∠CBA = 180 - 90 = 90°
Form an equation and solve
3x + 2x = 90
5x = 90
x = 18
Subt x = 18 into ∠ABD and ∠DBC.
∠ABD = 2(18) = 36°
∠DBC = 3(18) = 54°
Qn 12:
Adjacent angles on a straight line always add up to 180°. Form an equation and solve the top two first because if you solve the top and bottom, you will have two unknowns in one equation.
1st eqn: (9x +2) + (10x +7) = 180
19x + 9 = 180
19x = 171
x = 9
2nd eqn: (18y + 25) + (9x + 2) = 180
18y + 9x + 27 = 180
Subt in x = 9
18y = 180 - 9(9) - 27 = 72
y = 4
Qn 13:
Linear angles (or supplementary angles) are formed when two lines intersect each other at a point. They are adjacent to each other so the sum of angles of a linear pair is always equal to 180°.
Form an equation and solve
(7x - 3) + (x - 1) = 180
8x - 4 = 180
8x = 184
x = 23
Subt x = 23 into ∠A and ∠B
∠A = 7(23) - 3 = 158°
∠B = 23 - 1 = 22°