question for genius rank
Answers
We will use the angle sum property of a quadrilateral to find the measure of all the angles of the quadrilateral.
It is given that the angles of the quadrilateral are in the ratio 3: 5: 9: 13.
Let the four angles be 3x
, 5x
, 9x
, and 13x
respectively.
Now, the angle sum property of a quadrilateral states that the sum of the measures of the four interior angles of a triangle is always 360∘
.
Thus, the sum of the two four angles will be equal to 360∘
.
Therefore, we get
3x+5x+9x+13x=360∘
We will solve this equation to find the value of x
.
Adding the like terms in the equation, we get
⇒30x=360∘
Dividing both sides of the equation by 30, we get
⇒30x30=360∘30⇒x=12∘
∴
We get the value of x
as 12∘
.
Finally, we will substitute the value of x
to find the measures of all the angles of the quadrilateral.
Substituting x=12∘
in 3x
, we get the first angle of the quadrilateral as
3x=3×12∘=36∘
Substituting x=12∘
in 5x
, we get the second angle of the quadrilateral as
5x=5×12∘=60∘
Substituting x=12∘
in 9x
, we get the third angle of the quadrilateral as
9x=9×12∘=108∘
Substituting x=12∘
in 13x
, we get the fourth angle of the quadrilateral as
13x=13×12∘=156∘
∴
The measures of all the angles of the quadrilateral are 36∘, 60∘, 108∘and 156∘
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Step-by-step explanation:
It is a simple question
even a beginner rank can also solve it
Let ratio = 3x,5x,9x,13x
3x+5x+9x+13x= 360
30x = 360
x= 12
1st angle = 36°
2nd angle = 60°
3rd angle = 108°
4th angle = 156°