2 The angles of a quadrilateral are in the following ratio. Find the measurements of the angles.
b 1:2:3:4
a 2:3:4:6
c 1: 3: 6:8
Answers
☆ Solution ☆
b) 1 : 2 : 3 : 4
Let the ratios be x, 2x, 3x, 4x
As we know that :-
The sum of all angles of a quadrilateral = 360°
So,
1x + 2x + 3x + 4x = 360°
10x = 360°
x = 360/10
x = 36°
Thus,
The measures of each angles of quadrilateral are :-
x = 36°
2x = 2 × 36° = 72°
3x = 3 × 36° = 108°
4x = 4 × 36° = 144°
Hence,
The measure of each angles of a quadrilateral are 36°, 72°, 108° and 144°.
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a) 2 : 3 : 4 : 6
Let the ratios be 2x + 3x + 4x + 6x
As we know that :-
The sum of all angles of a quadrilateral = 360°
So,
2x + 3x + 4x + 6x = 360°
15x = 360°
x = 360/15
x = 24°
Thus,
The measures of each angles of quadrilateral are :-
2x = 2 × 24° = 48°
3x = 3 × 24° = 72°
4x = 4 × 24° = 96°
6x = 6 × 24° = 144°
Hence,
The measure of each angles of a quadrilateral are 48°, 72°, 96° and 144°.
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c) 1 : 3 : 6 : 8
Let the ratios be x + 3x + 6x + 8x
As we know that :-
The sum of all angles of a quadrilateral = 360°
So,
1x + 3x + 6x + 8x = 360°
18x = 360°
x = 360/18
x = 20°
Thus,
The measures of each angles of quadrilateral are :-
x = 20°
3x = 3 × 20° = 60°
6x = 6 × 20° = 120°
8x = 8 × 40° = 160°
Hence,
The measure of each angles of a quadrilateral are 20°, 60°, 120° and 160°.
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Answer:
Step-by-step explanation:
a) let the ratio be x =2 x ,3 x, 4 x,6 x
sum of all angles is 360
2 x +3 x+4 x+6 x=360
15 x=360
x=360/15
x=24
2 x=2*24=48 cm^2
3 x=3*24=72 cm^2
4 x=4*24=96 cm^2
6 x=6*24=144 cm^2
Hope , it helpful for u