Question

The measure of one angle of a parallelogram is 50⁰ . Find the measures of the remaining three angles .




Give me a proper answer

with full prperty anything

give me a proper answer​

Answer 1

Given :-

• Measure of one angle of a parallelogram is 50°

To Find :-

• Measure of the remaining three angles

Solution :-

❒ Here , Let ABCD be a parallelogram whose one angle ( let it be ∠A )  is of 50° , and we know that opposite angles of a parallelogram are equal and in this parallelogram

★ ∠A = ∠C  

★ ∠B = ∠D

➼ As , ( ∠A = ∠C ) and we're given the value of ∠A which is of 50°

   then , ∠C is also equal to 50°

❒ Here , ABCD is also a quadrilateral and we know that , sum of all angles of a quadrilateral is 360° .

~Let measure of angle ∠B and ∠D be x° ( they are equal )

★ ∠A + ∠B + ∠C + ∠D = 360°

( putting value of ∠A and ∠C as 50° and  ∠B and ∠D as x° )

→ 50° + 50° + x° + x° = 360°

→ 100° + 2x° = 360°

→ 2x = 360° - 100°

→ 2x = 260°

→ x = 260° ÷ 2

→ x = 130°

∴ ∠ A and ∠C = 50°

  ∠B and ∠D = 130°

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Answer 2

Question:-

The measure of one angle of a parallelogram is 50°. Find the measures of the remaining three angles.

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Given:-

• Measure of one angle of a parallelogram is 50°.

To Find:-

• The measures of the remaining three angles.

Diagram:-

$\begin{gathered}\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}\\\\\end{gathered}$

Solution:-

We know that

In a parallelogram opposite angles are equal opposite are parallel.Thus two angles on the same side are supplementary.

So,The ∠A is 50° so the ∠C will also equal to 50°.

Let the other two angles be x.

${\sf{ \red {: \longrightarrow 50 + 50 + x + x = 360 \degree}}} \\ \\ \\ {\sf{ \red{ : \longrightarrow 100 + 2x = 360 \degree}}} \\ \\ \\ {\sf{ \red{ : \longrightarrow 2x = 360° - 100}}} \\ \\ \\ {\sf{ \red{ : \longrightarrow x = 260° \div 2}}} \\ \\ \\ {\sf{ \red{ : \longrightarrow 130°}}}$

Hence,

∠A and ∠C = 50°

∠B and ∠D = 130°

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[Note : Kindly see the above diagram in web browser.(Brainly.in)

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