Question

Present age of the elder brother is 32 years and that of his younger brother is 12 years. Find the ratio and express in its Lowest form? a) Present age of elder brother to the present age of younger brother. b) Age of the elder brother to the age of younger brother,when younger brother was 4 years old. c) Age of younger brother to the age of elder brother after 10 years. d) Age of younger brother to the age of elder brother when elder brother was 30 years old.

Answer 1

Answer:

❍ The angles of the Quadrilateral are x°, (x – 10)°, (x + 30)° and 2x° respectively.

⠀⠀⠀\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}

†Asweknowthat:

⠀⠀⠀⠀

The sum of all angles of the Quadrilateral is 360°. Therefore,

\begin{gathered}:\implies\sf x + (x - 10)^\circ + (x + 30)^\circ + 2x = 360^\circ \\\\\\:\implies\sf x + x + x + 2x - 10 + 30 = 360^\circ \\\\\\:\implies\sf 3x + 2x - 10 + 30= 360^\circ \\\\\\:\implies\sf 5x + 20 = 360^\circ \\\\\\:\implies\sf 5x = 360^\circ - 20 \\\\\\:\implies\sf 5x = 340^\circ \\\\\\:\implies\sf x = \cancel\dfrac{340^\circ}{5} \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 68^\circ}}}}}\;\bigstar\end{gathered}

:⟹x+(x−10)

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+(x+30)

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+2x=360

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:⟹x+x+x+2x−10+30=360

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:⟹3x+2x−10+30=360

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:⟹5x+20=360

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:⟹5x=360

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−20

:⟹5x=340

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:⟹x=

5

340

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:⟹

x=68

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★

Hence,

First angle, x = 68°

Second angle, (x - 10)° = (68 - 10)° = 58°

Third angle, (x + 30)° = (68 + 30)° = 98°

Fourth angle, 2x = 2(68)° = 136°

\therefore{\underline{\sf{Hence, the\;greatest\;angle\;is\;\bf{136^\circ }.}}}∴

Hence,thegreatestangleis136

∘

.

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⠀

V E R I F I C A T I O N :

As we know that sum of the all angles of Quadrilateral is 360°. And, we've measure of each angle. So, Let's verify :

\begin{gathered}\dashrightarrow\sf a + b + c + d = 360^\circ \\\\\\\dashrightarrow\sf 68^\circ + 58^\circ + 98^\circ + 136^\circ = 360^\circ \\\\\\\dashrightarrow{\boxed{\underline{\sf{360^\circ = 360^\circ}}}}\end{gathered}

⇢a+b+c+d=360

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⇢68

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+58

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+98

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+136

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=360

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⇢

360

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=360

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\therefore{\underline{\textsf{\textbf{Hence Verified!}}}}∴

Hence Verified!

Answer 2

Answer:

This is your answer .

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