Question

5. In the given figure, find the value of x.

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Answer 1

Answer:

30

Step-by-step explanation:

complete line bd and then u can find angle dbc and angle bdc which are 70&80 resp.now subtract the sum of both of these from 180 u get 30°

Answer 2

AnswEr :

• x = 30°

Given :

• ∠ABC = 110°
• ∠EDC = 100°

To Find :

• The value of x.

Solution :

Construction : Exploring AB to m and n parallel to DE.

(Reference of Fig.)

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(3.5,5){\vector(1,0){3.5}}\put(2,4){\vector( - 1,0){3.5}}\qbezier(3.5,5)(3.5,5)(2.8,1.7)\qbezier(2,4)(2,4)(2.8,1.7)\multiput(2,4)(0.2,0){15}{\line(1, 0){0.1}}\put(5,4){\vector(1,0){0}}\qbezier(2.2,3.5)(1.4,3.8)(1.6,4)\qbezier(4.1,5)(3.7,4.4)(3.4,4.6)\qbezier(2.6,2.4)(2.7,2.55)(2.9,2.4)\put(-1.9,3.8){\bf A}\put(1.9,4.2){\bf B}\put(2.7,1.15){\bf C}\put(3.2,5.2){\bf D}\put(7,5.2){\bf E}\put(1,3.4){ \sf 110^\circ }\put(3.8,4.3){ \sf 100^\circ }\put(2.7,2.7){\sf x}\put(5.1,3.9){ \sf n }\put(3,4.1){ \sf m }\end{picture}$

• First, let's find the value of ∠CBm

➙ ∠CBm = 180° - ∠ABC [Straight line]

➙ ∠CBm = 180° - 110°

➙ ∠CBm = 70°

• Now, we need to find the value of ∠BmC

➙ ∠BmC = ∠nmD [vertically opposite angle]

We know that, the sum of interior angles of same side of transversal is 180°

• ∠nmD + ∠EDm = 180°
• ∠nmD + 100° = 180°
• ∠nmD = 180° - 100°
• ∠nmD = 80°

Hence, ∠BmC = 80°

In ∆BmC,

Sum of 3 angles of a triangle = 180°

➙ ∠BmC + ∠mCB + ∠CBm = 180°

➙ 80° + x + 70° = 180°

➙ 150° + x = 180°

➙ x = 30°