Question

Two angles of a triangle are in the ratio 2:3 if the third angle is 50,find the other two angles

Answer 1

we take
2:3 as 2x and 3x
by linear equation
2x+3x+50°=180
5x+50°=180
5x=180-50
5x=130
x=130÷5
x=26

then put 26 in place of x
2×26=52
3×26=78
the two angles are 52 and 78
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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°.

See Figure by question :

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

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

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°