Question

find X in the following figure
​

Answer 1

GIVEN:-

AB||CD

EXPLANATION:-

(7x+14)=4x+89  [ alternate angles are equal]

7x-4x=89-14

3x=75

x=75/3

x=25

Hence the value of x is 25.

EXTRA INFORMATION:-

(1) INTERIOR ANGLES:-

$\setlength{\unitlength}{8mm}\begin{picture}(0,0)\thicklines\put(2,4){\line(7,0){5}}\put(0,0){\line(6,0){6}}\qbezier(2,4)(2,4)(0,0)\qbezier(0.9,0)(1.1,0.6)(0.4,0.8)\qbezier(1.69,3.2)(2.5,3.2)(2.75,4)\put(3,0){\vector(3,0){1}}\put(5,4){\vector(3,0){1}}\end{picture}$

(2) ALTERNATE ANGLES:-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(0,3){2}{\line(1,0){4}}\qbezier(0,0)(0,0)(4,3)\qbezier(1,0)(1.2,0.35)(0.8,0.6)\qbezier(3,3)(2.8,2.65)(3.2,2.4)\put(2.5,0.02){\vector(1,0){0}}\put(1.5,3.02){\vector(-1,0){0}}\end{picture}$

(3)LINEAR PAIR:-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\put(5,1){\vector(1,0){4}}\put(5,1){\vector(-1,0){4}}\put(5,1){\vector(1,1){3}}\put(2,2){ \underline{\boxed{\large\sf a + b = 180^{\circ}} }}\put(4.5,1.3){ \sf a^{\circ} }\put(5.7,1.3){ \sf b^{\circ} }\end{picture}$

(4)CORRESPONDING ANGLES-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(2,5)\put(2,5){\line(1,0){4}}\put(1,2.5){\line(1,0){4}}\qbezier(1.8,2.5)(1.8,1.85)(0.75,1.88)\qbezier(2.8,5)(2.8,4.3)(1.75,4.3)\put(4,5){\vector(1,0){0}}\put(3.5,2.52){\vector(1,0){0}}\end{picture}$