Question

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

Answer:

• All four angles of parallelogram are 36°, 144°, 36° and 144°.

Step-by-step explanation:

Given :-

• Ratio of four angles of parallelogram is 1:4:1:4.

To find :-

• Four angles of parallelogram.

Solution :-

Let, All angles of parallelogram be 1x or x, 4x , x and 4x.

We know,

Sum of all four angles of parallelogram is 360°.

So,

$\rightarrow$ x + 4x + x + 4x = 360°

$\rightarrow$ 10x = 360°

$\rightarrow$ x = 360°/10

$\rightarrow$ x = 36°

Verification :-

$\rightarrow$ x + 4x + x + 4x = 360°

• Put x = 36°

$\rightarrow$ 36° + 4×36° + 36° + 4×36° = 360°

$\rightarrow$ 36° + 144° + 36° + 144° = 360°

$\rightarrow$ 360° = 360°

$\boxed{\sf Hence\: Verified.}$

Angles :

x = 36°

4x = 144°

x = 36°

4x = 144°

Therefore,

All four angles of parallelogram are 36°, 144°, 36° and 144°.

Answer 2

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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