Math, asked by saiketjaveer, 4 months ago

ABCD is a parallelogram in which ∠DAB = (3x - 50)° and ∠BCD = (x + 40)°, find the value of x. *​

Answers

Answered by Ladylaurel
6

Answer :-

The value of x is 45.

Step-by-step explanation :-

Given that,

\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf B}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf D}\qbezier(5.4,1)(5.2,1.48)(6.1,1.5)\qbezier(1.5,3.5)(1.7,3.2)(2.2,4)\put(2.2,3.5){\sf (3x - 50)^ \circ$}\put(3.9,1.5){\sf (x + 40)^\circ$}\end{picture}

Solution :-

We know that,

If in a parallelogram ABCD,

∠DAB = ∠BCD ........ opposite angles are equal

Therefore,

 \sf{\implies \: 3x - 50 = x + 40}

Transposing x to L.H.S and - 50 to R.H.S

 \sf{\implies \: 3x - x = 40 + 50}

 \sf{\implies \: 2x = 90}

 \sf{\implies \: x = \dfrac{90}{4}}

Dividing 90 and 2 with 2

 \sf{\implies \: x = \dfrac{45}{1}}

 \sf{\leadsto \: x = 45}

 \underline{\boxed{ \sf{Therefore, \: \: the \: \: value \: \: of \: \: x \: \: is \: \: 45}}}

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