a) 40^\circ,\;50^\circ\;\&\;90^\circ
b) 50^\circ,\;50^\circ\;\&\;80^\circ
c) 60^\circ,\;50^\circ\;\&\;70^\circ
d) 30^\circ,\;60^\circ\;\&\;90^\circ
correct answer is: a) 40^\circ,\;50^\circ\;\&\;90^\circ
Explanation
Here, the given ratio is 4\;:\;5\;:\;9.
We know, the sum of the angles of a triangle is 180°.
Let,
the angles of the triangle are represented by the expressions 4x, 5x and 9x, where 'x' is a variable.
According to the question,
\left(4x+5x+9x\right)=180°
\rightarrow 18x=180°
\rightarrow x=\large\frac{180^\circ}{18}
\rightarrow x=10°
So that,
The angles of the triangle are :
4x=(4×10°)=40°
5x=(5×10°)=50°
9x=(9×10°)=90°
Ans: The angles of the triangle are 40°, 50° and 90° respectively.
This math puzzle can be presented in many ways:
- Find the measures of the angles in a triangle when their ratio is 4 : 5 : 9.
- If the ratio of angles in a triangle is 4 : 5 : 9, what are the measures of the angles?
- Calculate the angles of a triangle with a ratio of 4 : 5 : 9.