Find the values of the unknowns ‘x ‘and y in the following diagrams.
i)
ii)
iii)
iv)
v)
vi)
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i) In ΔPQR
x° + 50° = 120° (exterior angle property)
x°= 120°- 50°
x°= 70°
Also ∠P + ∠Q +∠R = 180° (angle – sum property)
70° + 50° + y° = 180°
120° + y° = 180°
y° = 180° – 120°
y° = 60°
(OR)
y° + 120° = 1800 (linear pair of angles)
y° = 180°- 120°
∴ y° = 60°
ii) In the figure ΔRST,
x° = 80° (vertically opposite angles)
also ∠R + ∠S + ∠T = 180° (angle – sum property)
80° + 50°+ y°= 180°
130° + y° = 180°
y° = 180° – 130°
∴ y° = 50°
iii) m ΔMAN,
x° = ∠M + ∠A (exterior angle property)
x° = 50° + 60°
x° = 110°
Also x° + y° = 180°
110°+ y°= 180°
y° = 180° – 110°
y° = 70°
(OR)
in ΔMAN,
∠M + ∠A + ∠N = 180° (angle – sum property )
50° + 60° + y° = 180°
110° + y° = 180°
y° = 180°- 110°
∴ y° = 70°
v) In the figure ΔABC,
x° = 60° (vertically opposite angles)
∠A + ∠B + ∠ACB = 180° (angle – sum property)
y° + 30° + 60° = 180°
y° + 90° = 180°
y° = 180° – 90°
∴ y° = 90°
v) In the figure ΔEFG,
y° = 90° (vertically opposite angles)
Also in ΔEFG;
∠F + ∠E + ∠G = 180° (angle – sum property)
∴ x° + x° + y° = 180
2x° + 90° = 180°
2x° = 180°- 90°
2x° = 90°
x° = 90°/2
∴ x° = 45°
vi) In the figure ΔLET,
∠L = ∠T = ∠E = x° (vertically opposite angles)
Also in ΔLET
∠L + ∠E + ∠T = 180° (angle – sum property)
x° + x° + x° = 180°
3x° = 180°
x° = 180°/3
x° = 60°