in a quadrilateral, if it's four angles are in the ratio 5:2:4:7 then the sum if measures of the first two smaller angles is__________
Answers
✬ Sum = 120 ✬
Step-by-step explanation:
Given:
- The four angles of a quadrilateral are in ratio 5:2:4:7.
To Find:
- What is the sum of measure of first two smaller angles ?
Solution: Let x be the common in given ratio and angles of quadrilateral be ∠A , ∠B , ∠C and ∠D.
- ∠A = 5x , ∠B = 2x
- ∠C = 4x , ∠D = 7x
As we know that the sum of all interior angles of a quadrilateral is of 360°. Therefore,
∠A + ∠B + ∠C + ∠D = 360°
5x + 2x + 4x + 7x = 360°
18x = 360°
x = 360/18
x = 20°
So,
➛ ∠A = 5x = 5(20) = 100°
➛ ∠B = 2x = 2(20) = 40°
➛ ∠C = 4x = 4(20) = 80°
➛ ∠D = 7x = 7(20) = 140°
Now, arranging the values of angles in ascending order:-
- 40° , 80° , 100° , 140°
Here, First Smaller angle = 40° & Second smaller angles = 80°
∴ Their sum = 40° + 80° = 120°
Hence, the sum of measure of first two smaller angles is 120° .
Given :-
In a quadrilateral ,
The four angles are in the ratio of 5 : 2 : 4 : 7
Required to find :-
- Sum of the measures of the first two smaller angles ?
Conditions used :-
- Sum of all angles in a quadrilateral = 360°
Solution :-
Given that :-
In a quadrilateral ,
The four angles are in the ratio of 5 : 2 : 4 : 7
we need to find the sum of the measures of first two smaller angles .
So,
Let consider ;
Ratio of the 4 angles = 5 : 2 : 4 : 7
So,
Let ,
- 1st angle be 5x°
- 2nd angle be 2x°
- 3rd angle be 4x°
- 4th angle be 7x°
According to the conditions of the quadrilateral ;
Sum of all four angles in a quadrilateral = 360°
5x° + 2x° + 4x° + 7x° = 360°
18x° = 360
x° = 360°/18
x° = 20°
So,
The actual measurements of the 4 angles are ;
- 1st angle = 5x° = 5(20)° = 100°
- 2nd angle = 2x° = 2(20)° = 40°
- 3rd angle = 4x° = 4(20)° = 80°
- 4th angle = 7x° = 7(20)° = 140°
From the above we can conclude that ;
The smallest angles are 2nd angle and 3rd angle
So,
Sum of first two smaller angles =
=> 1st angle + 2nd angle
=> 40° + 80°
=> 120°
Therefore,
Sum of first two smaller angles = 120°
Extra Knowledge :-
The different types of quadrilateral are ;
- 1. Parallelogram
- 2. Trapezium
- 3. Rhombus
- 4. Rectangle
- 5. Square
- 6. Kite
A quadrilateral is a 2nd geometrical figure which is bounded by 4 line segments .
The quadrilateral is also considered to be the 2nd polygon if we consider triangle as the 1st polygon .
Each quadrilateral has a unique property when compared to other quadrilaterals .