Question

Two angles of a triangle are in the ratio 2:3 . If the third angle is 500 , find the other angles

Answer 1

How is the the 3rd angle 500 if the angles sum property of triangles is only till 180 degrees?

Answer 2

SOLUTION :

$\bf{\large{\underline{\bf{Given\::}}}}}$

Two angles of a triangle are in the ratio 2:3. If the third angle is 50°.

Attach Figure :

$\setlength{\unitlength}{0.8cm}\begin{picture}(6,5)\thicklines\put(1,0.5){\line(2,1){3}}\put(4,2){\line(-2,1){2}}\put(2,3){\line(-2,-5){1}}\put(0.7,0.3){ A }\put(4.05,1.9){ B }\put(1.7,2.95){ C }\put(3.1,2.5){ 50\degree }\put(1.3,1.7){ \sf\:\:\:\:3r }\put(2.5,1.05){ \:\:\:\sf2r }\end{picture}$

$\bf{\large{\underline{\bf{Explanation\::}}}}}$

We know that sum of all sides of triangle will be 180°

A/q

$\longrightarrow\sf{2r+3r+50\degree=180\degree}\\\\\longrightarrow\sf{5r+50\degree=180\degree}\\\\\longrightarrow\sf{5r=180\degree-50\degree}\\\\\longrightarrow\sf{5r=130\degree}\\\\\longrightarrow\sf{r=\cancel{130\degree/5}}\\\\\longrightarrow\bf{r=26\degree}$

Thus;

• 1st angle = 2r = 2 × 26° = 52°
• 2nd angle = 3r = 3 × 26° = 78°
• 3rd angle = 50°