Question

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Answer 1

Correct Question:-

• The four angles of a parallelogram ABCD are in the ratio of 1:4:1:4. Find all the four angles.

AnswEr :-

• $\boxed{\blue{\sf{\star{\:\:All\:four\:angles\:of\:Parallelogram \:is\:36⁰,144⁰,36⁰\:and\:144⁰}}}}$

Explanation:-

Given :-

• The four angles of a parallelogram ABCD are in the ratio of 1:4:1:4.

To Find :-

• The all four angles of parallelogram.

☆ Figure related to the question:-

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

Solution :-

☆ Let the four angles of parallelogram be -:

1st angle -: ( Angle )¹ = 1 x ⁰

2nd angle -: ( Angle )² = 4 x ⁰

3rd angle-: ( Angle)³ = 1 x ⁰

4th angle -; ( Angle )⁴ = 4 x ⁰ .................[1]

As we know that ,

$\boxed{\blue{\sf{\star{\:Sum \:of\:all\:four\:angles\:of\:Parallelogram \:is\:360⁰}}}}$

or ,

$\boxed{\blue{\sf{\star{\:(Angle)_{1} +( Angle)_{2}+ (Angle )_{3}+ (Angle)_{4} =\:360⁰}}}}$

Here ,

1st angle -: ( Angle )¹ = 1 x ⁰

2nd angle -: ( Angle )² = 4 x ⁰

3rd angle-: ( Angle)³ = 1 x ⁰

4th angle -; ( Angle )⁴ = 4 x ⁰ .................[From 1]

Now ,

• $\pink{\sf{\rightarrow {1x + 4x + 1x + 4x = 360⁰ }}}$

• $\pink{\sf{\rightarrow { 2x + 8x = 360⁰ }}}$

• $\pink{\sf{\rightarrow {10x = 360⁰ }}}$

• $\pink{\sf{\rightarrow {x =\frac { 360}{10} }}}$

• $\pink{\sf{\rightarrow {x = 36⁰ }}}$

Therefore,

$\boxed{\blue{\sf{\star{\:x = 36⁰}}}}$

Now ,

☆ Four Angles of parallelogram are :-

• 1st angle -: ( Angle )¹ = 1 x = 1 × 36 = 36⁰
• 2nd angle -: ( Angle )² = 4 x = 4 × 36 = 144⁰
• 3rd angle-: ( Angle)³ = 1 x = 1 × 36 = 36⁰
• 4th angle -; ( Angle )⁴ = 4 x = 4 × 36⁰

Hence ,

$\boxed{\blue{\sf{\star{\:\:All\:four\:angles\:of\:Parallelogram \:is\:36⁰,144⁰,36⁰\:and\:144⁰}}}}$

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Answer 2

Step-by-step explanation:

let the angles be x

so parallelogram degree is 360

so 1x:4x:1x:4x=360

so 1x:1x=180

2x=180

x=180/2=90

so the angles 1:1=90,90

4x+4x=180

8x=180

x=180/8=22.5

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