Math, asked by vandanapohkar, 6 months ago

if opposite angles of a parallelogram is (3x-40) and 2x. find all angles​

Answers

Answered by Ladylaurel
9

Solution:

  • Let the opposite angles of the parallelogram be ∠A and ∠C.

  • Given, opposite angles of a Parallelogram = (3x-40) and 2x.

We know that,

 \boxed{ \sf{opposite \: angles \: are \: equal}}

From the property of parallelogram.

\setlength{\unitlength}{1cm} \thicklines \begin{picture}(10,10) \qbezier(0,0)(5,0)(5,0) \qbezier(0,0)(1,2.5)(1,2.5) \qbezier(5,0)(6,2.5)(6,2.5) \qbezier(1,2.5)(6,2.5)(6,2.5)\put( - 0.4, - 0.3){ \large{A}}\put(5, - 0.3){ \large{B}}\put(5.9,2.7){ \large{C}}\put(0.8, 2.7){ \large{D}}\qbezier(0.08,0.3)(0.5,1)(0.8,0)\put(0.5,0.6){ \large{(2x) }}\qbezier(5.1,2.5)(4.5,1.8)(5.8,2)\put(4,1.5){ \large{(3x-40)}}\end{picture}

Accordingly,

  \implies \: 3x - 40 = 2x

By transposing 2x to L.H.S and 40 to R.H.S

 \implies \: 3x - 2x = 40

\implies \: x = 40

  \sf{\therefore \: The \: value \: of \:  x \: is \: 40}

  • The measure of angles are:-

 \longrightarrow \: (3x - 40)

\longrightarrow (40 \times 3) - 40

\longrightarrow 120 - 40

\longrightarrow \: 80

∴ The opposite angles ( ∠A and ∠C ) of the parallelogram are 80°

  • The measure of other opposite angles

(∠B and ∠D ) are:-

⟹ 180° - 80°

⟹ 100°

∴ ∠B and ∠D = 100°

Now, Verification

⟹ ∠A + ∠B + ∠C + ∠D = 360°

⟹ 80° + 100° + 80° + 100° = 360°

⟹ 180 + 180 = 360

⟹ 360 = 360.

☆ Required Answer:

  • ∠A = 80°
  • ∠B = 100°
  • ∠C = 80°
  • ∠D = 100°
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