Question

the two adjacent angles of a parallelogram measure (2x+50), (3x+20)the value of xis..​

Answer 1

Answer:

Measure of adjacent angles of a

parallelogram = 180

2x+50+3x+20 = 180

5x+70 = 180

5x = 110

x = 22

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Answer 2

Solution:-

Let the opposite angles of the parallelogram be ∠A and ∠B

We know that adjacent angles are supplementary.

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf A}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf B}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf D}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf C}\qbezier(1.5,1)(1.6,1.4)(1.1,1.5)\qbezier(5.5,1)(5.6,1.5)(6.05,1.4)\put(4,1.6){\bf (3x+20)}\put(1.5,1.6){\bf (2x+50)}\end{picture}$

According to the question,

$2x + 50 + 3x + 20 = 180$

$2x + 3x = 180 - 20 - 50$

$5x = 180 - 70$

$5x = 110$

$x = \dfrac{110}{5}$

$x = 22$

$\boxed{ \boxed{The \: value \: of \: x \: is \: 22}}$

Now, Let's find the measure of angles:-

• ( 2x + 50 )

= ( 2 × 22 + 50 )

= ( 44 + 50 )

= 94°

• ( 3x + 20 )

= ( 3 × 22 + 20 )

= ( 66 + 20 )

= 86°