Question

In fig. l ll m find out x​

Answer 1

Hello Friend.

Here is your answer below,,

we know a straight line makes an angle 180° so now we draw the line of 40° is meet to m line then we will find a triangle of 60° , 40° and 80°.

so it will make a 80 ° angle with the 3x+10 angle

so tha

3x +10 + 80 = 180

3x +90 = 180

3x =180 - 90

3x = 90

x = 30°

I hope that helps

Answer 2

$\setlength{\unitlength}{1cm}\begin{picture}(8,6)\multiput(0,0)(0,2){2}{\line(1,0){10}}\put(4,0){\line(1,1){1}}\put(4,2){\line(1,-1){1}}\put(4.4,0.13){ 60\textdegree }\put(4.4,1.68){ 40\textdegree }\put(3.1, 0.88){ (3x+10)\textdegree }\multiput(0,-0.1)(0,2.02){2}{ < }\multiput(9.8,-0.1)(0,2.02){2}{ > }\put(10.2,-0.1){ m }\put(10.2,1.9){ l }\end{picture}$

First we may draw a line, say 'n', parallel to 'l' and 'm', passing through the vertex of the angle.

$\setlength{\unitlength}{1cm}\begin{picture}(8,6)\multiput(0,0)(0,2){2}{\line(1,0){10}}\put(4,0){\line(1,1){1}}\put(4,2){\line(1,-1){1}}\put(4.4,0.13){ 60\textdegree }\put(4.4,1.68){ 40\textdegree }\put(3.1, 0.88){ (3x+10)\textdegree }\multiput(0,-0.1)(0,1.011){3}{ < }\multiput(9.8,-0.1)(0,1.011){3}{ > }\put(10.2,-0.1){ m }\put(10.2,1.9){ l }\put(0,1){\line(1,0){10}}\put(10.2,0.9){ n }\end{picture}$

Since  l ║ m ║ n,  by alternate angles, the angle having measurement  3x+ 10  will be split.

$\setlength{\unitlength}{1cm}\begin{picture}(8,6)\multiput(0,0)(0,2){2}{\line(1,0){10}}\put(4,0){\line(1,1){1}}\put(4,2){\line(1,-1){1}}\multiput(4.4,0.13)(-0.3,0.5){2}{ 60\textdegree }\multiput(4.4,1.68)(-0.32,-0.6){2}{ 40\textdegree }\multiput(0,-0.1)(0,1.011){3}{ < }\multiput(9.8,-0.1)(0,1.011){3}{ > }\put(10.2,-0.1){ m }\put(10.2,1.9){ l }\put(0,1){\line(1,0){10}}\put(10.2,0.9){ n }\end{picture}$

From this, we get,

(3x + 10)° = 40° + 60°

(3x + 10)° = 100°

3x = 100° - 10°

3x = 90°

x = 90° / 3

x = 30°

Hence,  30°  is the answer.