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Answers
Step-by-step explanation:
4- 130°
5-110°
6-85°
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Step-by-step explanation:
(i) Sum of angles of quadrilateral = 360°
Let the 2 angles be 'a' and 'b'. (Let them in your figure.)
Sum of angles = 360°
x + a + 140° + b = 360°
Let us find values of 'a' and 'b'.
(As 'a' and 140° is a linear pair so their sum would be 180°)
a + 130° = 180°
a = 180° - 130°
a = 50°
('b' and 130° is linear pair, so their sum = 180°)
b + 140° = 180°
b = 180° - 140°
b = 40°
Now let us find value of x,
Sum of angles = 360°
x + a + 140° + b = 360
x + 50° + 140° + 40° = 360°
x + 230° = 360°
x = 360° - 230°
x = 130°
ANSWER is = x = 130°
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(ii) Find x.
In your figure, Let the 4 interior angles be a, b, c, d.
Let us find 'a' , 'b' , 'c' , 'd'.
a + 120° = 180° (as it is a linear pair)
a = 180° - 120°
a = 60°
b + 50° = 180° (as it is a linear pair)
b = 180° - 50° = 130°
c + 80° = 180°
c = 180° - 80° = 100°
d = 180° - x
Sum of all angles of quadrilateral = 360°
a + b + c + d = 360°
60° + 130° + 100° + 180°-x = 360°
470° - x = 360°
470° = 360° + x
x = 470° - 360°
ANSWER is ; x = 110°
Verifying -
a + b + c+ d = 360°
60° + 130°+ 100° + 180° - x = 360°
60° + 130° + 100° + 180° - 110° = 360°
470° - 110° = 360°
360° = 360°
LHS = RHS
Hence , our answer is correct.
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(iii) Let the 3 interior angles which are not given be a, b, c in your figure.
a = 180° - 55° = 125° ( As it is a linear pair)
b = 180° - 130° = 50°
c = 180° - y
The other angle is given which is of 90°
Sum of angles = 360°
a + b + c + 90 = 360
125 + 50 + 180 - y + 90 = 360
445 - y = 360
445 = 360 + y
y = 445 - 360
ANSWER = y = 85
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